Protocol-Based Fault Detection for Discrete Delayed Systems With Missing Measurements: The Uncertain Missing Probability Case

Abstract

This paper is concerned with the protocol-based fault detection problem for a class of discrete systems with mixed time delays and missing measurements under uncertain missing probabilities. The phenomenon of missing measurements is characterized by a set of Bernoulli random variables, where each sensor could have individual missing probability and the corresponding occurrence probability could be uncertain. In order to mitigate the communication load of the network and reduce the incidence of the data collisions in the engineering reality, the round-robin (RR) protocol is employed to regulate the data transmission orders. The purpose of the addressed problem is to design a fault detection filter such that, in the simultaneous presence of mixed time delays, missing measurements, and RR protocol mechanism, the resulted filtering error system is asymptotically mean-square stable with a satisfactory $H_{\infty }$ performance. In particular, some sufficient conditions are derived in terms of certain matrix inequalities and the explicit expression of the required filter parameters is proposed. Finally, a numerical example is employed to illustrate the effectiveness of the designed fault detection scheme.