Contraction Analysis of Almost Surely Monotone Discrete-Time Systems With Unknown Time Delay
Open accessAbstract
In this paper, we utilize monotonicity to simplify contraction analysis of discrete-time nonlinear time-delay systems with parameters following stochastic processes. First, we extend the concept of almost sure monotonicity to the time-delay systems, which can be verified via analysis of the corresponding prolonged systems. Next, we introduce a novel notion of uniform incremental asymptotic stability (UIAS) in the first moment to the time-delay systems and develop its sufficient condition. By virtue of almost sure monotonicity, if this condition holds, the time-delay systems are UIAS in the first moment for any finite length of delay. Moreover, the proposed result suggests that UIAS in the first moment has a strong connection with stability of the averaged deterministic systems. We formalize this observation for almost surely cooperative systems by establishing the equivalence between UIAS and uniform incremental asymptotic mean stability.
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Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
Smith, H. L. (2008) · Mathematical surveys and monographs · doi:10.1090/surv/041 · Cited by 2,345 · see citing works
Contraction Analysis of Nonlinear SystemsPreprint
Slotine, J.-J. E. (1999) · Cited by 1,540 · see citing works
Angeli, D., & Sontag, E. D. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.817920 · Cited by 683 · see citing works
Nonnegative and Compartmental Dynamical Systems
Haddad, W. M., Chellaboina, V.-S., & Hui, Q. (2010) · Princeton University Press eBooks · doi:10.1515/9781400832248 · Cited by 537 · see citing works
A Differential Lyapunov Framework for Contraction Analysis
Forni, F., & Sepulchre, R. J. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2013.2285771 · Cited by 332 · see citing works
Measure Theory and Probability Theory
Athreya, K. B., & Lahiri, S. N. (2006) · Springer eBooks · doi:10.1007/978-0-387-35434-7 · Cited by 298 · see citing works
Separable Lyapunov functions for monotone systems: Constructions and limitations
Dirr, G., Ito, H., Rantzer, A., & Rüffer, B. S. (2015) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2015.20.2497 · Cited by 67 · see citing works
On Contraction Analysis for Non-linear Systems
Lohmiller, W., & Slotine, J.-J. E. (1998) · Automatica · doi:10.1016/s0005-1098(98)00019-3 · Cited by 58 · see citing works
Stabilization of positive Markov jump systems
Guo, Y. (2016) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2016.06.026 · Cited by 57 · see citing works
Stability Analysis of Monotone Systems via Max-Separable Lyapunov Functions
Feyzmahdavian, H. R., Besselink, B., & Johansson, M. (2017) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2017.2727282 · Cited by 46 · see citing works
A contractive approach to separable Lyapunov functions for monotone systems
Coogan, S. (2019) · Automatica · doi:10.1016/j.automatica.2019.05.001 · Cited by 39 · see citing works
Distributed Economic MPC With Separable Control Contraction Metrics
Wang, R., Manchester, I. R., & Bao, J. (2017) · IEEE Control Systems Letters · doi:10.1109/lcsys.2017.2708660 · Cited by 36 · see citing works
Contraction Analysis of Monotone Systems via Separable Functions
Kawano, Y., Besselink, B., & Cao, M. (2019) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2019.2944923 · Cited by 32 · see citing works
Self-citationIncremental Versus Differential Approaches to Exponential Stability and Passivity
Kawano, Y., & Besselink, B. (2024) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2024.3385036 · Cited by 22 · see citing works
Self-citationContraction Analysis of Discrete-Time Stochastic Systems
Kawano, Y., & Hosoe, Y. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3283678 · Cited by 20 · see citing works
Self-citationDistributed Nonlinear Control Design Using Separable Control Contraction Metrics
Shiromoto, H. S., Revay, M., & Manchester, I. R. (2018) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2018.2885270 · Cited by 19 · see citing works
Non-Euclidean Contraction Theory for Monotone and Positive Systems
Jafarpour, S., Davydov, A., & Bullo, F. (2022) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2022.3224094 · Cited by 14 · see citing works
Contraction analysis of virtually positive systems
Kawano, Y., & Cao, M. (2022) · Systems & Control Letters · doi:10.1016/j.sysconle.2022.105358 · Cited by 14 · see citing works
Self-citationNovel Stability Conditions for Nonlinear Monotone Systems and Consensus in Multiagent Networks
Deplano, D., Mauro Franceschelli, A., & Giua, A. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3246419 · Cited by 11 · see citing works
Delay-Independent Asymptotic Stability in Monotone Systems
Devane, E., & Lestas, I. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2015.2498137 · Cited by 9 · see citing works
Contraction Analysis of Differentially Positive Discrete-Time Stochastic Systems
Kawano, Y., & Hosoe, Y. (2025) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2025.3543562 · Cited by 8 · see citing works
Self-citation$\mathcal {K}$-Monotonicity and Feedback Synthesis for Incrementally Stable Networks
Kawano, Y., & Forni, F. (2024) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2024.3391871 · Cited by 7 · see citing works
Self-citationPath-Based Stability Analysis for Monotone Control Systems on Proper Cones
Kawano, Y., & Besselink, B. (2021) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2021.3118327 · Cited by 6 · see citing works
Self-citationMonotonicity and Contraction on Polyhedral Cones
Jafarpour, S., & Coogan, S. (2024) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2024.3454258 · Cited by 5 · see citing works
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Research works printed but not linked: 1
- Bullo, 2022, Contraction Theory for Dynamical Systems
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- Authors
- Kawano, Y., & Hosoe, Y.
- Affiliations
- Hiroshima University (JP)
- Kyoto University (JP)
- Venue
- IEEE Control Systems Letters
- Published
- 2025
- Volume
- 9
- Pages
- 426-431
- ISSN
- 2475-1456 (ISSN-L)
- OpenAlex
- W4410771883
- Cited by
- 1
- References
- 24
- Citations by year
- 2026: 1
- FWCI
- 0.37
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- IEEE Control Systems Letters (publishedVersion, cc-by-nc-nd)
- Funders
- JST FOREST Program (JPMJFR222E)
- JSPS KAKENHI (21H04875, 24K00910, 23K26127)
- JST PRESTO (JPMJPR2127)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Physical Sciences › Engineering › Control and Systems Engineering › Control and Stability of Dynamical Systems
- Keywords
- contraction analysis, discrete-time nonlinear systems, time-delay systems, unknown time delay, stochastic parameters, collaborative systems
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