Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays

Abstract

This paper is concerned with the fault detection (FD) problem for a class of discrete-time stochastic systems with channel fadings, randomly occurring multiple communication delays, and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.