Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.