State‐dependent switching control of delayed switched systems with stable and unstable modes

Abstract

In this paper, the problem of switching stabilization for a class of delayed switched systems is studied by using state-dependent switching control. Some sufficient conditions for asymptotic stability of delayed switched systems are derived, which are based on the Lyapunov functional method. The derived stability conditions can be applied for delayed switched systems with partial or all unstable modes. Moreover, a typical time delay called leakage delay existing in the negative feedback term of a system are also considered. Two numerical examples, that is, a switched system with two unstable modes and a switched system with delayed feedback control, are given to show the effectiveness of the main results. such that the following inequality holds:

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