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Stability theory for hybrid dynamical systems
Abstract
We first formulate a model for hybrid dynamical systems which covers a very large class of systems and which is suitable for the qualitative analysis of such systems. Next, we introduce the notion of an invariant set for hybrid dynamical systems and we define several types of (Lyapunov-like) stability concepts for an invariant set. We then establish sufficient conditions for uniform stability, uniform asymptotic stability, exponential stability, and instability of an invariant set of hybrid dynamical systems. Under some mild additional assumptions, we also establish necessary conditions for some of the above stability types (converse theorems). In addition to the above, we also establish sufficient conditions for the uniform boundedness of the motions of hybrid dynamical systems (Lagrange stability). To demonstrate the applicability of the developed theory, we present specific examples of hybrid dynamical systems and we conduct a stability analysis of some of these examples.
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Cited by
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 3,281
Goebel, R., Sanfelice, R. G., & Teel, A. R. (2009) · IEEE Control Systems · doi:10.1109/mcs.2008.931718 · Cited by 1,656
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 1,625
Asynchronously switched control of switched linear systems with average dwell time
Zhang, L., & Gao, H. (2010) · Automatica · doi:10.1016/j.automatica.2010.02.021 · Cited by 787
Controllers for reachability specifications for hybrid systems
Lygeros, J., Tomlin, C., & Sastry, S. (1999) · Automatica · doi:10.1016/s0005-1098(98)00193-9 · Cited by 608
Metadata
- Authors
- Ye, H., Michel, A. N., & Hou, L.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1998-04
- Volume
- 43
- Issue
- 4
- Pages
- 461-474
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2566720177
- Cited by
- 815
- References
- 0
- FWCI
- 53.06
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ye, H., Michel, A. N., & Hou, L. (1998). Stability theory for hybrid dynamical systems. IEEE Transactions on Automatic Control. https://doi.org/10.1109/9.664149
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