Hybrid Dynamical Systems
Abstract
Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Hybrid control refers to hierarchically organized systems that choose among discrete control modes at higher levels, and for each of these modes, different continuous controllers operate at lower levels.
“Hybrid control refers to hierarchically organized systems that choose among discrete control modes at higher levels, and for each of these modes, different continuous controllers operate at lower levels (Branicky et al., 1998; Goebel et al., 2009).”
From Lessons for Robotics From the Control Architecture of the Octopus (2022) · cites this paper as Goebel et al., 2009
Cites
Optimization and Nonsmooth Analysis
Clarke, F. H. (1990) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971309 · Cited by 10,435 · see citing works
Switching in Systems and Control
Liberzon, D. (2003) · Systems & control · doi:10.1007/978-1-4612-0017-8 · Cited by 7,066 · see citing works
Synchronization a universal concept in nonlinear sciences
PIKOVSKY, A. S., Rosenblum, M. G., & Kurths, J. (2001) · Cited by 5,640 · see citing works
Theory of Impulsive Differential Equations
Lakshmikantham, V., Байнов, Д. Д., & Simeonov, P. S. (1989) · WORLD SCIENTIFIC eBooks · doi:10.1142/0906 · Cited by 4,846 · see citing works
Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks
Tabuada, P. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.904277 · Cited by 4,732 · see citing works
Rockafellar, R. T., & Wets, R. J. ‐. (1998) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-02431-3 · Cited by 4,082 · see citing works
Basic problems in stability and design of switched systems
Liberzon, D., & Morse, A. S. (1999) · IEEE Control Systems · doi:10.1109/37.793443 · Cited by 3,650 · see citing works
Aubin, J., & Cellina, A. (1984) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-69512-4 · Cited by 3,402 · see citing works
Supervisory Control of a Class of Discrete Event Processes
Ramadge, P. J., & Wonham, W. M. (1987) · SIAM Journal on Control and Optimization · doi:10.1137/0325013 · Cited by 3,375 · see citing works
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
Branicky, M. S. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.664150 · Cited by 3,297 · see citing works
A linear matrix inequality approach to H ∞ control
Gahinet, P. M., & Apkarian, P. (1994) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.4590040403 · Cited by 3,244 · see citing works
Dynamic Equations on Time Scales
Böhner, M., & Peterson, A. C. (2001) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-0201-1 · Cited by 2,939 · see citing works
Hahn, W. (1967) · Springer eBooks · doi:10.1007/978-3-642-50085-5 · Cited by 2,766 · see citing works
Smooth stabilization implies coprime factorization
Sontag, E. D. (1989) · IEEE Transactions on Automatic Control · doi:10.1109/9.28018 · Cited by 2,748 · see citing works
Stability of switched systems with average dwell-time
Hespanha, J. P., & Morse, A. S. (2003) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.1999.831330 · Cited by 2,600 · see citing works
The general problem of the stability of motion
Lyapunov, A. M. (1992) · International Journal of Control · doi:10.1080/00207179208934253 · Cited by 2,581 · see citing works
The Stability of Dynamical Systems
Salle, J. P. L. (1976) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970432 · Cited by 2,103 · see citing works
Synchronization of Pulse-Coupled Biological Oscillators
Mirollo, R. E., & Strogatz, S. H. (1990) · SIAM Journal on Applied Mathematics · doi:10.1137/0150098 · Cited by 2,078 · see citing works
Nonsmooth Analysis and Control Theory
Clarke, F. H., Ledyaev, Y. S., Stern, R. J., et al. (1998) · Springer eBooks · doi:10.1007/b97650 · Cited by 2,003 · see citing works
Henzinger, T. A. (2002) · Proceedings - Symposium on Logic in Computer Science · doi:10.1109/lics.1996.561342 · Cited by 1,857 · see citing works
Stability analysis of networked control systems
Walsh, G. C., Ye, H., & Bushnell, L. G. (2002) · IEEE Transactions on Control Systems Technology · doi:10.1109/87.998034 · Cited by 1,698 · see citing works
Perspectives and results on the stability and stabilizability of hybrid systems
DeCarlo, R. A., Branicky, M. S., Pettersson, S., & Lennartson, B. (2000) · Proceedings of the IEEE · doi:10.1109/5.871309 · Cited by 1,628 · see citing works
Sync: The Emerging Science of Spontaneous Order
Goldenfeld, N. D. (2004) · Physics Today · doi:10.1063/1.1784276 · Cited by 1,528 · see citing works
Supervisory control of families of linear set-point controllers - Part I. Exact matching
Morse, A. S. (1996) · IEEE Transactions on Automatic Control · doi:10.1109/9.539424 · Cited by 1,478 · see citing works
Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems
Byrnes, C. I., Isidori, A., & Willems, J. C. (1991) · IEEE Transactions on Automatic Control · doi:10.1109/9.100932 · Cited by 1,377 · see citing works
A Unified Framework for Hybrid Control: Model and Optimal Control Theory
Branicky, M. S., Borkar, V. S., & Mitter, S. K. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.654885 · Cited by 1,313 · see citing works
An introduction to hybrid dynamical systems
van der Schaft, A. J., & Schumacher, H. (2000) · Lecture notes in control and information sciences · doi:10.1007/bfb0109998 · Cited by 1,225 · see citing works
Discontinuous dynamical systems
Cortés, J. (2008) · IEEE Control Systems · doi:10.1109/mcs.2008.919306 · Cited by 1,104 · see citing works
Stabilization with relaxed controls
Artstein, Z. (1983) · Nonlinear Analysis · doi:10.1016/0362-546x(83)90049-4 · Cited by 1,000 · see citing works
Uniform Stability of Switched Linear Systems: Extensions of LaSalle's Invariance Principle
Hespanha, J. P. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.825641 · Cited by 929 · see citing works
Some Extensions of Liapunov's Second Method
LASALLE, J. P. (1960) · IRE Transactions on Circuit Theory · doi:10.1109/tct.1960.1086720 · Cited by 914 · see citing works
A Smooth Converse Lyapunov Theorem for Robust Stability
Lin, Y., Sontag, E. D., & Wang, Y. (1996) · SIAM Journal on Control and Optimization · doi:10.1137/s0363012993259981 · Cited by 874 · see citing works
Putting energy back in control
Ortega, R. S., van der Schaft, A. J., Mareels, I., & Maschke, B. M. (2001) · IEEE Control Systems · doi:10.1109/37.915398 · Cited by 869 · see citing works
Systems with impulse effect : stability, theory, and applications
Байнов, Д. Д., & Simeonov, P. S. (1989) · Medical Entomology and Zoology · Cited by 853 · see citing works
(2001) · Springer eBooks · doi:10.1007/3-540-47710-1 · Cited by 838 · see citing works
Dynamical properties of hybrid automata
Lygeros, J., Johansson, K. H., Simić, S. N., et al. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2002.806650 · Cited by 820 · see citing works
Stability theory for hybrid dynamical systems
Ye, H., MICHEL, A. N., & Hou, L. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.664149 · Cited by 816 · see citing works
Unilateral Contact and Dry Friction in Finite Freedom Dynamics
Moreau, J. J. (1988) · Springer eBooks · doi:10.1007/978-3-7091-2624-0_1 · Cited by 782 · see citing works
Synchronous Rhythmic Flashing of Fireflies. II.
Buck, J. (1988) · The Quarterly Review of Biology · doi:10.1086/415929 · Cited by 735 · see citing works
Mathematical aspects of heart physiology
Peskin, C. S. (1975) · Courant Institute of Mathematical Sciences, New York University eBooks · Cited by 605 · see citing works
Impulsive and Hybrid Dynamical Systems
Haddad, W. M., Chellaboina, V.-S., & Nersesov, S. G. (2006) · Princeton University Press eBooks · doi:10.1515/9781400865246 · Cited by 601 · see citing works
Pomet, J. (1992) · Systems & Control Letters · doi:10.1016/0167-6911(92)90019-o · Cited by 598 · see citing works
On the theory of stability of motion
Matrosov, V. M. (1962) · Journal of Applied Mathematics and Mechanics · doi:10.1016/0021-8928(62)90189-2 · Cited by 566 · see citing works
A Lyapunov-Like Characterization of Asymptotic Controllability
Sontag, E. D. (1983) · SIAM Journal on Control and Optimization · doi:10.1137/0321028 · Cited by 563 · see citing works
On the regularization of Zeno hybrid automata
Johansson, K. H., Egerstedt, M., Lygeros, J., & Sastry, S. (1999) · Systems & Control Letters · doi:10.1016/s0167-6911(99)00059-6 · Cited by 543 · see citing works
Stability of Switched Systems with Average Dwell-Time 1
Hespanha, P., & Morse, A. S. (1999) · Cited by 529 · see citing works
Jurdjevic, V., & Quinn, J. P. (1978) · Journal of Differential Equations · doi:10.1016/0022-0396(78)90135-3 · Cited by 484 · see citing works
Brogliato, B. (1999) · Communications and control engineering/Communications and control engineering series · doi:10.1007/978-1-4471-0557-2 · Cited by 481 · see citing works
HYSDEL—A Tool for Generating Computational Hybrid Models for Analysis and Synthesis Problems
Torrisi, F. D., & Bemporad, A. (2004) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2004.824309 · Cited by 437 · see citing works
Discontinuous Dynamical Systems: A tutorial on solutions, nonsmooth analysis, and stabilityPreprint
Cortés, J. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0901.3583 · Cited by 399 · see citing works
Solutions to hybrid inclusions via set and graphical convergence with stability theory applications
Goebel, R. K., & Teel, A. R. (2006) · Automatica · doi:10.1016/j.automatica.2005.12.019 · Cited by 382 · see citing works
Self-citationTopological Complexity of Motion Planning
Färber, M. (2003) · Discrete & Computational Geometry · doi:10.1007/s00454-002-0760-9 · Cited by 380 · see citing works
A Lyapunov Proof of an Improved Maximum Allowable Transfer Interval for Networked Control Systems
Carnevale, D., Teel, A. R., & Nešić, D. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.895913 · Cited by 377 · see citing works
Self-citationGlobally asymptotically stable ‘PD+’ controller for robot manipulators
Paden, B. E., & PANJA, R. (1988) · International Journal of Control · doi:10.1080/00207178808906130 · Cited by 375 · see citing works
Sufficient lyapunov-like conditions for stabilization
Tsinias, J. (1989) · Mathematics of Control Signals and Systems · doi:10.1007/bf02551276 · Cited by 347 · see citing works
Acoustic Synchrony: Two Mechanisms in the Snowy Tree Cricket
Walker, T. J. (1969) · Science · doi:10.1126/science.166.3907.891 · Cited by 344 · see citing works
New results and examples in nonlinear feedback stabilization
Byrnes, C. I., & Isidori, A. (1989) · Systems & Control Letters · doi:10.1016/0167-6911(89)90080-7 · Cited by 340 · see citing works
Fundamental properties of reset control systems
Beker, O., Hollot, C. V., Chait, Y., et al. (2004) · Automatica · doi:10.1016/j.automatica.2004.01.004 · Cited by 335 · see citing works
Synchronization and computation in a chaotic neural network
Hansel, D., & Sompolinsky, H. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.718 · Cited by 333 · see citing works
Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability
Sanfelice, R. G., Goebel, R. K., & Teel, A. R. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.910684 · Cited by 321 · see citing works
Self-citationApplications of hysteresis switching in parameter adaptive control
Morse, A. S., Mayne, D. Q., & Goodwin, G. C. (1992) · IEEE Transactions on Automatic Control · doi:10.1109/9.159571 · Cited by 321 · see citing works
Nonlinear norm-observability notions and stability of switched systems
Hespanha, J. P., Liberzon, D., Angeli, D., et al. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.841937 · Cited by 314 · see citing works
Applications of hysteresis switching in parameter adaptive control
Morse, A. S., Mayne, D. Q., & Goodwin, G. C. (2002) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.1991.261417 · Cited by 311 · see citing works
The general problem of the stability of motion
SMITH, M. C. (1995) · Automatica · doi:10.1016/0005-1098(95)90022-5 · Cited by 305 · see citing works
Supervisory control of hybrid systems
Koutsoukos, X., Antsaklis, P. J., Stiver, J. A., & Lemmon, M. D. (2000) · Proceedings of the IEEE · doi:10.1109/5.871307 · Cited by 302 · see citing works
Time-varying Feedback Stabilization of Car-like Wheeled Mobile Robots
Samson, C. (1993) · The International Journal of Robotics Research · doi:10.1177/027836499301200104 · Cited by 294 · see citing works
Asymptotic Stability and Smooth Lyapunov Functions
Clarke, F. H., Ledyaev, Y. S., & Stern, R. J. (1998) · Journal of Differential Equations · doi:10.1006/jdeq.1998.3476 · Cited by 285 · see citing works
Impulse differential inclusions: a viability approach to hybrid systems
Aubin, J., Lygeros, J., Quincampoix, M., et al. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/9.981719 · Cited by 284 · see citing works
Stable walking of a 7-dof biped robot
Plestan, F., Grizzle, J. W., Westervelt, E. R., et al. (2003) · IEEE Transactions on Robotics and Automation · doi:10.1109/tra.2003.814514 · Cited by 264 · see citing works
Stabilization of nonholonomic integrators via logic-based switching
Hespanha, J. P., & Morse, A. S. (1999) · Automatica · doi:10.1016/s0005-1098(98)00166-6 · Cited by 254 · see citing works
Qualitative Theory of Hybrid Dynamical Systems
Matveev, A. S., & Savkin, A. V. (2000) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-1364-2 · Cited by 248 · see citing works
Examples when nonlinear model predictive control is nonrobust
Grimm, G., Messina, M. J., Tuna, S. E., & Teel, A. R. (2004) · Automatica · doi:10.1016/j.automatica.2004.04.014 · Cited by 240 · see citing works
Self-citationStability properties of reset systems
Nešić, D., Zaccarian, L., & Teel, A. R. (2008) · Automatica · doi:10.1016/j.automatica.2007.11.014 · Cited by 236 · see citing works
Self-citationH/sub infinity / control and filtering for sampled-data systems
Sun, W., Nagpal, K. M., & Khargonekar, P. P. (1993) · IEEE Transactions on Automatic Control · doi:10.1109/9.233150 · Cited by 230 · see citing works
Differential automata and their discrete simulators
Tavernini, L. (1987) · Nonlinear Analysis · doi:10.1016/0362-546x(87)90034-4 · Cited by 226 · see citing works
Discontinuous differential equations, I
Hájek, O. (1979) · Journal of Differential Equations · doi:10.1016/0022-0396(79)90056-1 · Cited by 225 · see citing works
Differential Equations and Dynamical Systems
I., E., Hale, J. K., & LASALLE, J. P. (1968) · Mathematics of Computation · doi:10.2307/2004696 · Cited by 215 · see citing works
Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation
Byrnes, C. I., & Isidori, A. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.817926 · Cited by 208 · see citing works
On Liapounoff's Conditions of Stability
Massera, J. L. (1949) · Annals of Mathematics · doi:10.2307/1969558 · Cited by 206 · see citing works
Recent trends in the stability analysis of hybrid dynamical systems
MICHEL, A. N. (1999) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.739260 · Cited by 205 · see citing works
Global stabilization of nonlinear cascade systems
Seibert, P., & Suárez, R. (1990) · Systems & Control Letters · doi:10.1016/0167-6911(90)90056-z · Cited by 197 · see citing works
Smooth Lyapunov Functions for Hybrid Systems Part II: (Pre)Asymptotically Stable Compact Sets
Cai, C., & Goebel, R. K. (2008) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2008.919257 · Cited by 197 · see citing works
Self-citationOperational Semantics of Hybrid Systems
Lee, E. A., & Zheng, H. (2005) · Lecture notes in computer science · doi:10.1007/978-3-540-31954-2_2 · Cited by 195 · see citing works
Hybrid systems: Generalized solutions and robust stability
Goebel, R. K., Hespanha, J. P., Teel, A. R., et al. (2004) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)31194-1 · Cited by 194 · see citing works
Self-citationSmoothing derivatives of functions and applications
Wilson, F. (1969) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1969-0251747-9 · Cited by 183 · see citing works
Dynamics in Infinite Dimensions
Hale, J. K., Magalhães, L. T., & Oliva, W. M. (2002) · Applied mathematical sciences · doi:10.1007/b100032 · Cited by 177 · see citing works
Lorı́a, A., Panteley, E. V., Popovic, D., et al. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.841939 · Cited by 177 · see citing works
Hierarchical modeling and analysis of embedded systems
Alur, R., Dang, T., Esposito, J. M., et al. (2003) · Proceedings of the IEEE · doi:10.1109/jproc.2002.805817 · Cited by 172 · see citing works
A new asymptotic stability criterion for nonlinear time-variant differential equations
Aeyels, D., & Peuteman, J. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.701102 · Cited by 171 · see citing works
A Lyapunov characterization of robust stabilization
Ledyaev, Y. S., & Sontag, E. D. (1999) · Nonlinear Analysis · doi:10.1016/s0362-546x(98)00075-3 · Cited by 158 · see citing works
Differential Equations: A Dynamical Systems Approach
Hubbard, J., & West, B. (2013) · Texts in applied mathematics · doi:10.1007/978-1-4612-0937-9 · Cited by 151 · see citing works
Stability of Dynamical Systems: Continuous, Discontinuous, and Discrete Systems
Astolfi, A. (2007) · Medical Entomology and Zoology · Cited by 147 · see citing works
Smooth Lyapunov functions and robustness of stability for difference inclusions
Kellett, C. M., & Teel, A. R. (2004) · Systems & Control Letters · doi:10.1016/j.sysconle.2004.02.015 · Cited by 131 · see citing works
Self-citationAn LMI solution to the robust synthesis problem for multi-rate sampled-data systems
Lall, S., & Dullerud, G. E. (2001) · Automatica · doi:10.1016/s0005-1098(01)00167-4 · Cited by 128 · see citing works
An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control
Ryan, E. P. (1998) · SIAM Journal on Control and Optimization · doi:10.1137/s0363012996301701 · Cited by 119 · see citing works
Analysis of Zeno behaviors in a class of hybrid systems
Heymann, M. A., Lin, F., Meyer, G., et al. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2005.843874 · Cited by 119 · see citing works
Is there life after Zeno? Taking executions past the breaking (Zeno) point
Ames, A. D., Zheng, H., Gregg, R. D., et al. (2006) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2006.1656623 · Cited by 114 · see citing works
Smooth Lyapunov Functions for Hybrid Systems—Part I: Existence Is Equivalent to Robustness
Cai, C., Teel, A. R., & Goebel, R. K. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.900829 · Cited by 111 · see citing works
Self-citationOn the inversion of Ljapunov’s second theorem on stability of motion
Kurzweil, J. (1963) · Translations - American Mathematical Society/Translations · doi:10.1090/trans2/024/04 · Cited by 107 · see citing works
An invariance principle for nonlinear hybrid and impulsive dynamical systems
Chellaboina, V.-S., Bhat, S. P., & Haddad, W. M. (2003) · Nonlinear Analysis · doi:10.1016/s0362-546x(02)00316-4 · Cited by 103 · see citing works
Qualitative Theory of Dynamical Systems
MICHEL, A. N., Wang, A., Hu, B., et al. (2001) · CRC Press eBooks · doi:10.1201/9780203908297 · Cited by 103 · see citing works
Uniting Local and Global Controllers with Robustness to Vanishing Noise
Prieur, C. (2001) · Mathematics of Control Signals and Systems · doi:10.1007/pl00009880 · Cited by 99 · see citing works
A hybrid strategy for the feedback stabilization of nonholonomic mobile robots
Pomet, J., Thuilot, B., Bastin, G. L., et al. (2003) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.1992.220323 · Cited by 98 · see citing works
MODELICA — THE NEW OBJECT-ORIENTED MODELING LANGUAGE
Elmqvist, H., Otter, M., & Mattsson, S. E. (1998) · Cited by 98 · see citing works
On Input-to-State Stability of Impulsive Systems
Hespanha, J. P., Liberzon, D., & Teel, A. R. (2006) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2005.1582786 · Cited by 94 · see citing works
Self-citationRemarks on smooth feedback stabilization of nonlinear systems
Lee, K. K., & Arapostathis, A. (1988) · Systems & Control Letters · doi:10.1016/0167-6911(88)90038-2 · Cited by 90 · see citing works
Measure Driven Differential Inclusions
Silva, G. N., & Vinter, R. (1996) · Journal of Mathematical Analysis and Applications · doi:10.1006/jmaa.1996.0344 · Cited by 90 · see citing works
Invariance principles for switching systems via hybrid systems techniques
Goebel, R. K., Sanfelice, R. G., & Teel, A. R. (2008) · Systems & Control Letters · doi:10.1016/j.sysconle.2008.06.002 · Cited by 82 · see citing works
Self-citationResults on input-to-state stability for hybrid systems
Cai, C., & Teel, A. R. (2006) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2005.1583021 · Cited by 78 · see citing works
Self-citationSemidefinite lyapunov functions stability and stabilization
Iggidr, A., Kalitine, B. S., & Outbib, R. (1996) · Mathematics of Control Signals and Systems · doi:10.1007/bf01211748 · Cited by 76 · see citing works
On the inversion of Ljapunov's second theorem on stability of motion
Kurzweil, J. (1955) · Czechoslovak Mathematical Journal · doi:10.21136/cmj.1955.100158 · Cited by 76 · see citing works
Aristotle's Physics: a guided study
(1995) · Choice Reviews Online · doi:10.5860/choice.33-1591 · Cited by 74 · see citing works
Generalized solutions to hybrid dynamical systems
Sanfelice, R. G., Goebel, R. K., & Teel, A. R. (2008) · ESAIM Control Optimisation and Calculus of Variations · doi:10.1051/cocv:2008008 · Cited by 74 · see citing works
Self-citationGoh, T. B., Li, Z., Chen, B. M., et al. (2001) · IEEE Transactions on Control Systems Technology · doi:10.1109/87.911374 · Cited by 72 · see citing works
On systems of ordinary differential equations with measures as controls
Maso, G. D., & Rampazzo, F. (1991) · Differential and Integral Equations · doi:10.57262/die/1371225013 · Cited by 71 · see citing works
Singular Perturbations on the Infinite Interval
Hoppensteadt, F. C. (1966) · Transactions of the American Mathematical Society · doi:10.2307/1994672 · Cited by 70 · see citing works
Sufficient Conditions for the Existence of Zeno Behavior
Ames, A. D., Abate, A., & Sastry, S. (2006) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2005.1582237 · Cited by 69 · see citing works
Resetting Virtual Absorbers for Vibration Control
Bupp, R. T., Bernstein, D. S., Chellaboina, V.-S., et al. (2000) · Journal of Vibration and Control · doi:10.1177/107754630000600104 · Cited by 66 · see citing works
On stability properties of nonlinear systems with slowly varying inputs
Khalil, H. K., & Kokotović, P. V. (1991) · IEEE Transactions on Automatic Control · doi:10.1109/9.67301 · Cited by 65 · see citing works
Raff, T., & Allgöwer, F. (2007) · Mediterranean Conference on Control and Automation (MED) · doi:10.1109/med.2007.4433909 · Cited by 60 · see citing works
Rhythmic Feedback Control of a Blind Planar Juggler
Ronsse, R., Lefèvre, P., & Sepulchre, R. J. (2007) · IEEE Transactions on Robotics · doi:10.1109/tro.2007.900602 · Cited by 54 · see citing works
Energy- and Entropy-Based Stabilization for Lossless Dynamical Systems via Hybrid Controllers
Haddad, W. M., Chellaboina, V.-S., Hui, Q., et al. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.904452 · Cited by 49 · see citing works
A hybrid systems approach to trajectory tracking control for juggling systems
Sanfelice, R. G., Teel, A. R., & Sepulchre, R. J. (2007) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2007.4435010 · Cited by 48 · see citing works
Self-citationToivonen, H. T. T., & SÅGFORS, M. F. (1997) · International Journal of Control · doi:10.1080/002071797224757 · Cited by 46 · see citing works
A new approach to the design of mode switching control in hard disk drive servo systems
Venkataramanan, V., Chen, B. M., Lee, T. H., et al. (2002) · Control Engineering Practice · doi:10.1016/s0967-0661(02)00037-0 · Cited by 45 · see citing works
Systems with Lebesgue Sampling
Åström, K. J., & Bernhardsson, B. (2007) · Springer eBooks · doi:10.1007/3-540-36106-5_1 · Cited by 44 · see citing works
A component-based approach to modeling and simulating mixed-signal and hybrid systems
Liu, J., & Lee, E. A. (2002) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/643120.643125 · Cited by 42 · see citing works
Lyapunov-Like Conditions for the Existence of Zeno Behavior in Hybrid and Lagrangian Hybrid Systems
Lamperski, A., & Ames, A. D. (2007) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2007.4435003 · Cited by 42 · see citing works
Asynchronous hybrid systems with jumps – analysis and synthesis methods
Dullerud, G. E., & Lall, S. (1999) · Systems & Control Letters · doi:10.1016/s0167-6911(99)00002-x · Cited by 41 · see citing works
Lyapunov characterization of Zeno behavior in hybrid systems
Goebel, R. K., & Teel, A. R. (2008) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2008.4738864 · Cited by 38 · see citing works
Self-citationContinuous selections of trajectories of hybrid systems
Broucke, M. E., & Arapostathis, A. (2002) · Systems & Control Letters · doi:10.1016/s0167-6911(02)00185-8 · Cited by 35 · see citing works
Simplicius on Aristotle's Physics 6
Konstan, D. (1989) · Cornell University Press eBooks · Cited by 33 · see citing works
Mousa, M., Miller, R. K., & MICHEL, A. N. (1986) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1986.1104346 · Cited by 32 · see citing works
Cadenced runs of impulse and hybrid control systems
Aubin, J., & Haddad, G. (2001) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.590 · Cited by 30 · see citing works
Robust Performance Verification of Adaptive Robust Controller for Hard Disk Drives
Taghirad, H. D., & Jamei, E. (2008) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2007.896502 · Cited by 30 · see citing works
Ames, A. D., Abate, A., & Sastry, S. (2007) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2007.4434891 · Cited by 29 · see citing works
Discrete-time control design with positive semi-definite Lyapunov functions
Grizzle, J. W., & Kang, J. (2001) · Systems & Control Letters · doi:10.1016/s0167-6911(01)00110-4 · Cited by 26 · see citing works
Zeno behavior in homogeneous hybrid systems
Goebel, R. K., & Teel, A. R. (2008) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2008.4739223 · Cited by 26 · see citing works
Self-citationSupervising a family of hybrid controllers for robust global asymptotic stabilization
Sanfelice, R. G., Teel, A. R., & Goebel, R. K. (2008) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2008.4739481 · Cited by 26 · see citing works
Self-citationConstructions of strict Lyapunov functions for discrete time and hybrid time-varying systems
Malisoff, M., & Mazenc, F. (2008) · Cited by 23 · see citing works
Stability of hybrid automata with average dwell time: an invariant approach
Mitra, S., & Liberzon, D. (2004) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2004.1430238 · Cited by 22 · see citing works
Hybrid Systems: Limit Sets and Zero Dynamics with a View Toward Output Regulation
Cai, C., Goebel, R. K., Sanfelice, R. G., et al. (2007) · Springer eBooks · doi:10.1007/978-3-540-74358-3_15 · Cited by 20 · see citing works
Self-citationRelaxation Results for Hybrid Inclusions
Cai, C., Goebel, R. K., & Teel, A. R. (2007) · Set-Valued Analysis · doi:10.1007/s11228-007-0067-3 · Cited by 16 · see citing works
Self-citationConstructions of strict Lyapunov functions for discrete time and hybrid time-varying systems
Malisoff, M., & Mazenc, F. (2007) · Nonlinear Analysis Hybrid Systems · doi:10.1016/j.nahs.2006.12.005 · Cited by 15 · see citing works
Smooth patchy control Lyapunov functions
Goebel, R. K., Prieur, C., & Teel, A. R. (2006) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2006.377706 · Cited by 11 · see citing works
Self-citationA nested Matrosov theorem for hybrid systems
Sanfelice, R. G., & Teel, A. R. (2008) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2008.4586938 · Cited by 10 · see citing works
Self-citationOn robust, global stabilization of the attitude of an underactuated rigid body using hybrid feedback
Teel, A. R., & Sanfelice, R. G. (2008) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2008.4586937 · Cited by 6 · see citing works
Self-citationComplex Hybrid Systems: Stability Analysis for Omega Limit Sets
Cai, C., Rafal, G., Sanfelice, R. G., et al. (2006) · Chinese Control Conference (CCC) · doi:10.1109/chicc.2006.4347525 · Cited by 4 · see citing works
Self-citationA Globally Stabilizing Time-switching Control Strategy for an Underactuated Rigid Body
Casagrande, D., Astolfi, A., & Parisini, T. (2007) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2007.4282562 · Cited by 4 · see citing works
Generalised Hybrid Trajectory Spaces
Collins, P. (2006) · Data Archiving and Networked Services (DANS) · Cited by 3 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Periodic Event-Triggered Control for Linear Systems
Heemels, W. P. M. H., Donkers, M. C. F., & Teel, A. R. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2012.2220443 · Cited by 1,407 · see citing works
Self-citationA Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems
Liu, T., & Jiang, Z.-P. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2015.2396645 · Cited by 398 · see citing works
Neural Network-Based Event-Triggered State Feedback Control of Nonlinear Continuous-Time Systems
Sahoo, A., Xu, H., & Jagannathan, S. (2016) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2015.2416259 · Cited by 292 · see citing works
Perspectives on the integration between first-principles and data-driven modeling
Bradley, W., Kim, J., Kilwein, Z., Blakely, L., Eydenberg, M., Jalvin, J., Laird, C., & Boukouvala, F. (2022) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2022.107898 · Cited by 231 · see citing works
Practical verification of decision-making in agent-based autonomous systems
Dennis, L. A., Fisher, M., Lincoln, N. K., Lisitsa, A., & Veres, S. M. (2016) · Automated Software Engineering · doi:10.1007/s10515-014-0168-9 · Cited by 102 · see citing works
Lessons for Robotics From the Control Architecture of the Octopus
Sivitilli, D. M., Smith, J. R., & Gire, D. H. (2022) · Frontiers in Robotics and AI · doi:10.3389/frobt.2022.862391 · Cited by 13 · see citing works
“Hybrid Control Hybrid control refers to hierarchically organized systems that choose among discrete control modes at higher levels, and for each of these modes, different continuous controllers operate at lower levels (Branicky et al., 1998; Goebel et al., 2009).”
Background
- Authors
- Goebel, R., Sanfelice, R. G., & Teel, A. R.
- Affiliations
- Loyola University Chicago (US)
- University of Arizona (US)
- University of California, Santa Barbara (US)
- Venue
- IEEE Control Systems
- Published
- 2009-04
- Volume
- 29
- Issue
- 2
- Pages
- 28-93
- ISSN
- 1066-033X (ISSN-L)
- 1941-000X
- OpenAlex
- W2099308299
- Cited by
- 1,656
- References
- 150
- Citations by year
- 2026: 36 · 2025: 67 · 2024: 67 · 2023: 66 · 2022: 61 · 2021: 118 · 2020: 117 · 2019: 115 · 2018: 106 · 2017: 109 · 2016: 129 · 2015: 117 · 2014: 152 · 2013: 120 · 2012: 103
- FWCI
- 147.01
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Control Systems (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Formal Methods in Verification
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Keywords
- hybrid dynamical systems, robust stability, hybrid control, asymptotic stability, stabilizing controllers, data perturbation, external disturbances, measurement error
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
