Reliable ℌ∞ control for time-varying stochastic systems with randomly occurring sensor failures

This paper is concerned with the reliable control problem for a class of time-varying stochastic system subject to possible sensor failures, while satisfying H_∞ performance requirement. The sensor failures are assumed to happen in a random way, namely, randomly occurring sensor failures (ROSF), and the failure probability is governed by a random variable obeying the Bernoulli distribution. The purpose of this problem is to design an output feedback controller such that the closed-loop system meets the desired H_∞ performance over a finite horizon. Sufficient condition for the existence of the desired controller is given, where the feedback gains at each time point k can be obtained by solving certain convex optimization problems iteratively. A numerical computing algorithm is presented, and then a simulation example is given to illustrate the effectiveness and applicability of the proposed algorithm.