Indefinite Lyapunov–Razumikhin Functions-Based Stability and Event-Triggered Control of Switched Nonlinear Time-Delay Systems

Abstract

This brief studies stability and event-triggered stabilization of switched nonlinear time-varying systems by virtue of Lyapunov-Razumikhin functions (LRFs), when the requirement on derivative of LRFs to non-positive is relaxed. A class of such LRFs is first constructed for the input-to-state stability (ISS) of nonlinear time-delay systems. Using multiple LRFs with indefinite derivatives, the ISS of switched nonlinear time-delay systems is presented under average dwell time switching. Then, a nonlinear event-triggered controller is designed for the underlying systems, and it is pointed out that the Zeno phenomenon can be avoided under the proposed controller. Moreover, an event-triggered control is introduced for the systems subject to disturbances to reach the ISS. Finally, one example is given to verify the validity of the proposed approaches.