Reliable H ∞ control for discrete uncertain time-delay systems with randomly occurring nonlinearities: the output feedback case

Abstract

This article is concerned with the reliable H ∞ output feedback control problem against actuator failures for a class of uncertain discrete time-delay systems with randomly occurred nonlinearities (RONs). The failures of actuators are quantified by a variable varying in a given interval. RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilistic way according to a Bernoulli distributed white sequence with a known conditional probability. The time-varying delay is unknown with the given lower and upper bounds. Attention is focused on the analysis and design of an output feedback controller such that, for all possible actuator failures, RONs, time-delays as well as admissible parameter uncertainties, the closed-loop system is exponentially mean-square stable and also achieves a prescribed H ∞ performance level. 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.