A gain-scheduled approach to fault-tolerant control for discrete-time stochastic delayed systems with randomly occurring actuator faults

This paper is concerned with the probability-dependent gain-scheduled fault-tolerant control problem for a class of discrete-time stochastic nonlinear delayed systems with randomly occurring actuator faults (ROAFs) by utilizing parameter-based Lyapunov functional. The occurrence of the possible actuator faults is modeled by a random sequence in terms of a time-varying Bernoulli distribution with measurable probability in real time. The nonlinear functions are assumed to satisfy the sector nonlinearities. The purpose of the addressed fault-tolerant control problem is to design a controller with scheduled gains such that, for the admissible ROAFs, nonlinearities, time delays and noises, the closed-loop system is exponentially mean-square stable while preserving a guaranteed H∞ performance. By using the semi-definite programme method, the time-varying fault-tolerant controller is derived which is dependent on the occurrence probability of the actuator faults. Therefore, the main results lead to less conservatism than those obtained by conventional methods with fixed controller gains only. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures.