Yazar "Wisniewski, Rafael" seçeneğine göre listele

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    Almost global stability of nonlinear switched system with stable and unstable subsystems
    (IEEE, 2020) Kıvılcım, Ayşegül; Karabacak, Özkan; Wisniewski, Rafael
    This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.
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    Almost global stability of nonlinear switched systems with mode-dependent and edge-dependent average dwell time
    (Elsevier Sci Ltd, 2021) Kıvılcım, Ayşegül; Karabacak, Özkan; Wisniewski, Rafael
    It has recently been shown that almost global stability of nonlinear switched systems can be characterized using multiple Lyapunov densities. This has been accomplished for switched systems subject to a minimum dwell time or an average dwell time constraint. In this paper, as an extension of the aforementioned results, we provide a sufficient condition on mode-dependent and edge-dependent average dwell time to ensure almost global stability of a nonlinear switched system. The relations between average dwell time, mode-dependent, and edge-dependent average dwell time have been discussed. The obtained results for nonlinear switched systems imply the existing results for linear switched systems. (C) 2021 Elsevier Ltd. All rights reserved.
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    Almost global stability of nonlinear switched systems with time-dependent switching
    (Institute of Electrical and Electronics Engineers Inc., 2020) Karabacak, Özkan; Kıvılcım, Ayşegül; Wisniewski, Rafael
    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.