Robust reliable control for discrete-time-delay systems with stochastic nonlinearities and multiplicative noises

This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete-time stochastic nonlinear time-delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well-studied nonlinear functions as special cases. The time-varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed-loop system is exponentially mean-square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach.