## Stability analysis of switched time delay systems.(English)Zbl 1157.93462

Summary: This paper addresses the asymptotic stability of switched time delay systems with heterogeneous time invariant time delays. Piecewise Lyapunov-Razumikhin functions are introduced for the switching candidate systems to investigate the stability in the presence of an infinite number of switchings. We provide sufficient conditions in terms of the minimum dwell time to guarantee asymptotic stability under the assumptions that each switching candidate is delay-independently or delay-dependently stable. Conservatism analysis is also provided by comparing with the dwell time conditions for switched delay-free systems. Finally, a numerical example is given to validate the results.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D20 Asymptotic stability in control theory 93C05 Linear systems in control theory 93C23 Control/observation systems governed by functional-differential equations

### Keywords:

asymptotic stability; switched systems; time delay; dwell time
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