Abstract
This study deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky-Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique) stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems.
Highlights
Switching systems are hybrid dynamical systems composed of subsystems with their own parameterizations subject to a rule orchestrating the switching law between the various subsystems
This study deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non commensurate constant internal point delays
A key motivation for studying switched systems is that many practical systems are inherently multi-model in the sense that several dynamic subsystems describe their whole behavior depending on multiple environmental factors[5]
Summary
Switching systems are hybrid dynamical systems composed of subsystems with their own parameterizations subject to a rule orchestrating the switching law between the various subsystems. The presence of internal delays leads to a large complexity in the resulting system’s dynamics since the whole dynamical system becomes infinite-dimensional This fact increases, in addition, the difficulty in the study of basic properties, like for instance controllability, observability, stability and stabilization and robustness, compared to the delay-free case since the transfer functions consist of transcendent numerator and denominator quasi-polynomials[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. The objective of this study is to investigate the stability and stabilization properties of linear switched time-delay dynamic systems subject to, in general, multiple incommensurate known internal point delays. Asymptotic stability independent of and dependent on the delays: Consider the time- varying switched linear dynamic system: Theorem 1: The following items hold: i.
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