Fault Detection Filter for Markov Jump Systems

2012 ◽  
Vol 503-504 ◽  
pp. 1488-1492 ◽  
Author(s):  
Yu Cai Ding ◽  
Hong Zhu ◽  
Shou Ming Zhong ◽  
Yu Ping Zhang
Keyword(s):  
Fault Detection ◽  
Transition Probabilities ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Fault Detection Filter ◽  
Partly Unknown Transition Probabilities ◽  
Attenuation Level ◽  
Jump Systems ◽  
Detection Filter

This paper deals with the problem of fault detection for Markov jump systems (MJSs) with time-varying delays and partly unknown transition probabilities. The aim of this paper is to design a fault detection filter such that the filtering error system is stochastically asymptotically stable with an attenuation level. By using the Lyapunov-Krasovskii functional, a sufficient condition for the existence of the desired fault detection filter is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

scholarly journals Robust H∞ Fault Detection for Networked Markov Jump Systems with Random Time-Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yanfeng Wang ◽  
Zuxin Li ◽  
Peiliang Wang ◽  
Zhe Zhou
Keyword(s):  
Time Delay ◽  
Fault Detection ◽  
Random Time ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Fault Detection Filter ◽  
Stochastically Stable ◽  
Sufficient And Necessary Conditions ◽  
Jump Systems ◽  
Detection Filter

This paper investigates the problem of robust H∞ fault detection for networked Markov jump systems with random time-delay which is introduced by the network. The random time-delay is modeled as a Markov process, and the networked Markov jump systems are modeled as control systems containing two Markov chains. The delay-dependent fault detection filter is constructed. Furthermore, the sufficient and necessary conditions which make the closed-loop system stochastically stable and achieve prescribed H∞ performance are derived. The method of calculating controller, fault detection filter gain matrices, and the minimal H∞ attenuation level is also obtained. Finally, one numerical example is used to illustrate the effectiveness of the proposed method.

scholarly journals Dynamic-Event-Based Fault Detection for Markov Jump Systems Under Hidden-Markov Mode Observation

2020 ◽  
Vol 24 (7) ◽  
pp. 917-924
Author(s):  
Xiaoxiao Xu ◽  
Xiongbo Wan ◽  
◽  
◽  
Keyword(s):  
Fault Detection ◽  
Hidden Markov ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Dynamic Event ◽  
Special Cases ◽  
Jump Systems ◽  
Hidden Markov Mode ◽  
Event Triggered

The fault detection (FD) problem is investigated for event-triggered discrete-time Markov jump systems (MJSs) with hidden-Markov mode observation. A dynamic-event-triggered mechanism, which includes some existing ones as special cases, is proposed to reduce unnecessary data transmissions to save network resources. Mode observation of the MJS by the FD filter (FDF) is governed by a hidden Markov process. By constructing a Markov-mode-dependent Lyapunov function, a sufficient condition in terms of linear matrix inequalities (LMIs) is obtained under which the filtering error system of the FD is stochastically stable with a prescribed H∞ performance index. The parameters of the FDF are explicitly given when these LMIs have feasible solutions. The effectiveness of the FD method is demonstrated by two numerical examples.

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