Delay-hybrid-dependent stability for systems with large delays

Xi-Ming Sun 1 Xue-Fang Wang 1 Frédéric Mazenc 2, 3
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : This paper investigates a problem of stability analysis for a class of nonlinear systems with a time-varying delay taking both large and small values in an alternating manner. This problem is a delay-dependent stability analysis one but it shares some features with delay-independent ones. Hence traditional stability analysis techniques for systems with delay do not apply. By building upon our previous works, we first introduce the concept of delay-hybrid-dependent stability, which grasps the features of the delays described above. To ease the problem we investigate, we represent the studied system as a system with a switched delay. Then by using switching techniques and Lyapunov-Krasovskii functionals (LKFs), we provide a new stability criterion. Next, in the linear context, we show how the needed LKFs can be constructed by developing an original design of LKFs.
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Xi-Ming Sun, Xue-Fang Wang, Frédéric Mazenc. Delay-hybrid-dependent stability for systems with large delays. IEEE transactions on systems, man, and cybernetics, Institute of Electrical and Electronics Engineers (IEEE), 2018, pp.1-12. ⟨hal-01849022⟩

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