Robust stability of switched nonlinear systems with delay and sampling

This article investigates the stability issue for a class of switched nonlinear systems whose control inputs include time delay and sampling. It is assumed that a stabilizing controller is predesigned for the nominal system such that it is stable under a certain switching signal. However, in the presence of input delay and sampling, the system may not be stable under the same stability criteria. Besides, the switching signals are discussed in two cases, that is, the switching signal of the system is transmitted to the controller in real time and only the sampled information of the switching signal is available to the controller at each sampling instant. For the latter, the asynchronous motions between the subsystems and the candidate controllers are caused and the closed-loop system is rewritten as sampled switched nonlinear delay system with an augmented switching signal. By constructing sampling interval-dependent Lyapunov–Krasovskii functional and using the theory of the asynchronous switched delay system, we establish the stability conditions on the switching signal which depends on the size of the delay, the upper bound of the sampling interval, and the dwell time. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.