Abstract
This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.
Highlights
This paper studies the input-to-state stability (ISS) of nonlinear switched systems
Switched systems are a special subclass of hybrid systems which consist of two components: a family of systems and a switching signal
We presented some new average dwell-time (ADT)-based sufficient conditions for ISS of switched systems via Lyapunov method involving indefinite derivative
Summary
Switched systems are a special subclass of hybrid systems which consist of two components: a family of systems and a switching signal. [32] proposed a new approach for ISS property of nonlinear systems It presents a new comparison principle for estimating an upper bound on the state of the system in which the derivative of the Lyapunov function may be indefinite, rather than negative definite, which improves the previous work on this topic greatly. To the best of our knowledge, there are few results on ISS of switched systems based on Lyapunov method involving indefinite derivative. Motivated by the above discussions, in this paper, we shall study the ISS property for switched systems via Lyapunov method involving indefinite derivative.
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