A Reduced-Order Fault Detection Filtering Approach for Continuous-Time Markovian Jump Systems with Polytopic Uncertainties

Lihong Rong,Xiuyan Peng,Biao Zhang

doi:10.1155/2017/4927453

Abstract

The fault detection (FD) reduced-order filtering problem is investigated for a family of continuous-time Markovian jump linear systems (MJLSs) with polytopic uncertain transition rates, which also include the totally known and partly unknown transition rates. Then, in accordance with the convexification techniques, a novel sufficient condition for the existence of FD reduced-order filter over MJLSs with deficient transition information is obtained in terms of linear matrix inequality (LMI), which can ensure the error augmented system with the FD reduced-order filter is randomly 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, the effectiveness of the proposed method is substantiated with two illustrative examples.

Highlights

Over the past few years, Markov jump linear systems (MJLSs) have been attracting extensive research attention in many engineering fields, such as energy system, solar thermal power generation system, networked control system, manufacturing system, and financial market system [1, 2]
We introduce an H∞ performance analysis criterion for the error augmented system (7) and further focus on the design of the fault detection (FD) reduced-order filter for MJLS (1) with deficient mode information
A fault detection approach is proposed for continuous-time MJLSs with deficient transition information

Summary

Introduction

Over the past few years, Markov jump linear systems (MJLSs) have been attracting extensive research attention in many engineering fields, such as energy system, solar thermal power generation system, networked control system, manufacturing system, and financial market system [1, 2]. The authors in [4] investigated a new approach to delay-dependent H∞ filtering for discrete-time Markovian jump systems with the exactly known, partially unknown, and uncertain TRs concurrently, which was more rational and general to research on the Complexity comprehensive analysis of MJLSs. But there are few research results about fault detection of Markovian jump systems with the exactly known, partially unknown, and uncertain TRs concurrently, and the loss of sensor or actuator information can be efficiently modeled by means of Markov chain frameworks. There are few research results about fault detection of Markovian jump systems with the exactly known, partially unknown, and uncertain TRs concurrently, and the loss of sensor or actuator information can be efficiently modeled by means of Markov chain frameworks This is the need to solve the main problem, which is one of the motivations for our research

Methods

Results

Conclusion