Almost global stability of nonlinear switched systems with time-dependent switching
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Tarih
2020
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Dergi ISSN
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Yayıncı
Institute of Electrical and Electronics Engineers Inc.
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
For a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of multiple Lyapunov densities for a nonlinear switched system implies almost global stability, in the same way as the existence of multiple Lyapunov functions implies global stability for nonlinear switched systems. In this paper, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell time constraint with an arbitrarily small dwell time. Specifically, as the main result, we show that a nonlinear switched system with a minimum dwell time is almost globally stable if there exist multiple Lyapunov densities that satisfy some compatibility conditions depending on the value of the minimum dwell time. This result can also be used to obtain a minimum dwell time estimate to ensure almost global stability of a nonlinear switched systems. In particular, the existence of a common Lyapunov density implies almost global stability for any arbitrary small minimum dwell time. The results obtained for continuous-time switched systems are based on some sufficient conditions for the almost global stability of discrete-time nonautonomous systems. These conditions are obtained using the duality between Frobenius-Perron operator and Koopman operator. © 1963-2012 IEEE.
Açıklama
Anahtar Kelimeler
Almost global stability, common Lyapunov density, minimum dwell time, multiple Lyapunov densities, nonlinear switched systems, Dynamical systems, Lyapunov functions, System stability, Almost global stability, Compatibility conditions, Frobenius-Perron operators, Global stability, Minimum dwell time, Multiple Lyapunov function, Non-autonomous system, Nonlinear switched systems, Continuous time systems
