Fault detection reduced-order filter design for discrete-time Markov jump system with deficient transition information

Lihong Rong,Xiuyan Peng,Biao Zhang

doi:10.1186/s13634-016-0374-7

Abstract

The paper addresses the fault detection (FD) problem for a class of discrete-time Markov jump linear systems (MJLSs) with deficient transition rates, which simultaneously considers the totally known, partly unknown, and uncertain transition rates. Then, in accordance with the linear matrix inequality (LMI) method and the convexification techniques, a sufficient condition for the existence of FD reduced-order filter over MJLSs with deficient transition information is obtained, which can ensure the error augmented system with the FD reduced-order filter is stochastically stable. In addition, a performance index is given to enhance the robustness of the residual system against deficient transition information and external disturbance, such that the error between the fault and the residual is made as small as possible to reinforce the faults sensitivity. Finally, an illustrative example is employed to show the effectiveness of the proposed design approach.

Highlights

During the past decades, Markov jump linear systems (MJLSs) have been received extensive interests in many engineering fields, such as energy system, solar thermal power generation system, networked control system, manufacturing system, financial market system [1, 2]
MJLSs are very appropriate to dynamical model systems whose property is subject to random sudden variant due to abrupt external disturbance, shifting of the action spots of a nonlinear system, and repairs of components, in order to ensure the nonlinear system stochastically exponentially stable, the author in [9] proposed a Markovian Lyapunov functional which was been successfully used in the nonlinear systems
The basic design idea of fault detection (FD) is to use the effective methods to generate a residual signal and to construct a common diagnostic residual evaluation function to compare with a beforehand threshold, an alarm of fault is generated when the value of system residual is larger than the threshold [30, 31]

Summary

Introduction

Markov jump linear systems (MJLSs) have been received extensive interests in many engineering fields, such as energy system, solar thermal power generation system, networked control system, manufacturing system, financial market system [1, 2]. In many practical applications, high-order models are frequently used to describe physical systems This brings many difficulties in design of the corresponding FD filter in order to detect faults in a timely way. To the knowledge of the authors, there are few results have been reported in the literature on the high-efficiency FD reduced-order filter design. This motivates us to study this work in order to reduce the complexity, computation time of the FD filter design process and save storage space, so as to improve the efficiency of the fault detection, which has great potential in practical applications

Methods

Conclusion