Filtering-Based Fault Detection for Stochastic Markovian Jump System with Distributed Time-Varying Delays and Mixed Modes

The problem of fault detection for stochastic Markovian jump system is considered. The system under consideration involves discrete and distributed time-varying delays, Ito-type stochastic disturbance, and different system and delay modes. The aim of this paper is to design a fault detection filter such that the fault detection system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a novel Lyapunov functional, a mix-mode-dependent sufficient condition is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

[1]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[2]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  S. Ding,et al.  An LMI approach to the design of fault detection filter for time-delay LTI systems with unknown inputs , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[4]  Visakan Kadirkamanathan,et al.  Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems , 2001, IEEE Trans. Syst. Man Cybern. Part C.

[5]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[6]  Jason L. Speyer,et al.  Optimal stochastic fault detection filter , 2003, Autom..

[7]  H. Ye,et al.  Fault detection for Markovian jump systems , 2005 .

[8]  Hong Wang,et al.  Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[10]  Maiying Zhong,et al.  Observer-Based Fault Detection for Networked Control Systems with Random Time-delays , 2006, First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC'06).

[11]  Ligang Wu,et al.  An LMI approach to fault detection and isolation filter design for Markovian jump system with mode-dependent time-delays , 2006, 2006 American Control Conference.

[12]  Lei Guo,et al.  Observer-based optimal fault detection using PDFs for time-delay stochastic systems , 2008 .

[13]  Ping Zhang,et al.  On fault detection in linear discrete-time, periodic, and sampled-data systems , 2008 .

[14]  Jitao Sun,et al.  H∞ filtering for a class of stochastic Markovian jump systems with impulsive effects , 2008 .

[15]  Hanyong Shao.  Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters , 2008 .

[16]  Zidong Wang,et al.  An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays , 2008 .

[17]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[18]  Fei Liu,et al.  Fuzzy model‐based fault detection for Markov jump systems , 2009 .

[19]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..

[20]  Peng Shi,et al.  Parity space-based fault detection for Markovian jump systems , 2009, Int. J. Syst. Sci..

[21]  Shengyuan Xu,et al.  H∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays , 2009, J. Frankl. Inst..

[22]  Donghua Zhou,et al.  Robust fault detection for networked systems with communication delay and data missing , 2009, Autom..

[23]  Hamid Reza Karimi,et al.  A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations , 2010, J. Frankl. Inst..

[24]  Jinliang Liu,et al.  H∞ filtering for Markovian jump systems with time-varying delays , 2010, 2010 Chinese Control and Decision Conference.

[25]  Max Q.-H. Meng,et al.  Robust H∞ exponential filtering for uncertain stochastic time-delay systems with Markovian switching and nonlinearities , 2010, Appl. Math. Comput..

[26]  Shengyuan Xu,et al.  Delay-dependent H∞ filtering for stochastic systems with Markovian switching and mixed mode-dependent delays , 2010 .

[27]  Qingling Zhang,et al.  Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays , 2010 .

[28]  Hamid Reza Karimi,et al.  Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities , 2010, Int. J. Control.

[29]  H. Su,et al.  H∞ filtering for singular Markovian jump systems with time delay , 2010 .

[30]  Chen Peng,et al.  Observer-based fault detection for networked control systems with network Quality of Services , 2010 .

[31]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[32]  Khashayar Khorasani,et al.  A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems , 2010, IEEE Transactions on Automatic Control.

[33]  Fei Liu,et al.  Gain-Scheduled Robust Fault Detection on Time-Delay Stochastic Nonlinear Systems , 2011, IEEE Transactions on Industrial Electronics.

[34]  Wei Xing Zheng,et al.  Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements , 2011, IEEE Transactions on Signal Processing.

[35]  Hong Wang,et al.  LMI-BASED FAULT DETECTION FUZZY OBSERVER DESIGN WITH MULTIPLE PERFORMANCE CONSTRAINTS FOR A CLASS OF NON-LINEAR SYSTEMS: COMPARATIVE STUDY , 2011 .

[36]  H. Momeni,et al.  Robust observer-based H∞ control of a Markovian jump system with different delay and system modes , 2011 .

[37]  H. Talebi,et al.  A Novel Simultaneous Fault Detection and Control Approach Based on Dynamic Observer , 2011 .

[38]  Fei Liu,et al.  Filtering-based robust fault detection of fuzzy jump systems , 2011, Fuzzy Sets Syst..

[39]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Caixia Liu,et al.  Finite-Time H∞ Filtering for Singular Stochastic Systems , 2012, J. Appl. Math..

[42]  Zhongqiu Wang,et al.  Fault Detection of Markov Jumping Linear Systems , 2012 .

[43]  Guoping Lu,et al.  Fault detection for state-delay fuzzy systems subject to random communication delay , 2012 .