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Zbl 1162.93393
de la Sen, M.; Ibeas, A.
Stability results for switched linear systems with constant discrete delays. (English)
[J] Math. Probl. Eng. 2008, Article ID 543145, 28 p. (2008). ISSN 1024-123X; ISSN 1563-5147/e

Summary: This paper investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwall's lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky-Lyapunov functional for all the above-mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time-varying systems are also discussed.

MSC 2000:: *93D20 Asymptotic stability of control systems
93C05 Linear control systems
93C15 Control systems governed by ODE

Keywords: Gronwall's lemma; global asymptotic stability; switching law; Krasovsky-Lyapunov functional

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Zentralblatt MATH Berlin [Germany]