H ∞ fault-tolerant control for switched linear parameter-varying systems: A parameter and state-dependent switching method with dwell time

Abstract

This article discusses the issue of H_∞ fault-tolerant control for switched linear parameter-varying systems with actuator failures using the multiple discretized parameter-dependent Lyapunov functions method. A key point of this work is to construct the multiple discretized parameter-dependent Lyapunov functions, which provide an effective tool for avoiding the Zeno behavior generated by the parameter and state-dependent switching approach. This is not a simple extension of traditional multiple Lyapunov functions because of the introduction of external parameter and dwell time. First, a switching strategy depending on the parameter, state and dwell time is proposed, which gets rid of the assumption of finite number of switchings on any finite time. Then, the parameter-dependent controller is designed which, together with the parameter and state-dependent switching law with dwell time, can guarantee the $H_{\infty }$ performance of the closed-loop switched linear parameter-varying system for all admissible actuator failures. Finally, a turbofan engine example is given to demonstrate the applicability of the main results.