Fault-tolerant Control Of Several Classes Of Switched Systems

Switched system is a special and important class of hybrid dynamical systems, which widely exists in engineering and practice. A switched system is generally described by several continuous-time subsystems or discrete-time subsystems and a switching law that coordinates the activation of each subsystems. The research of switched system is of great theoretical and practical meaning. The fault-tolerant control can improve the reliability of systems by reducing the effect generated from actuator failures. Finite-time stability, which focuses on the transient behavior over a finite interval, is different from the stability under Lyapunov meaning. This paper studies the finite-time fault-tolerant control problems of three classes of switched systems. All summarizes as follows:First, the finite-time fault-tolerant control for a kind of discrete-time linear switched systems is investigated. By using multiple Lyapunov functions and average dwell-time method, the state feedback controller is designed to guarantee the finite-time stability of switched systems with possible actuator failures in the permissible range. The results are proved to be valid by simulation.Second, we discuss the finite-time stability of continuous time linear time invariant systems with possible controller failures. The system with possible controller failures is regarded as switched systems contain a stable subsystem and an unstable subsystem. Then, the conceptions of unavailability rate of the controller and the average time interval between controller failures are defined. By using a multiple Lyapunov functions, we showed that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures is large enough, the finite-time stability of the system is guaranteed.Last, the finite-time fault-tolerant stabilization of nonlinear switched systems is studied. The nonlinear parts of the systems are assumed to be stable under some reasonable assumptions. By constructing combined Lyapunov functions with the adjustable parameters, and using average dwell-time method, the sufficient condition of robust fault-tolerant stability for nonlinear switched systems with possible actuator failures in the permissible range is obtained. The conclusions are tested by simulations.In the end, the full text of the work is summarized, and some directions for future research are proposed.