Reliable exponential H∞ filtering for singular Markovian jump systems with time‐varying delays and sensor failures

• Published in: International journal of robust and nonlinear control Vol. 28; no. 14; pp. 4230 - 4245
• Main Authors: Liu, Guobao, Xu, Shengyuan, Park, Ju H., Zhuang, Guangming
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.09.2018
• Subjects: Decay rate; Delay; Error detection; exponential H∞ filtering; Failure; Filtration; H-infinity control; Linear matrix inequalities; Markov processes; Matrix methods; sensor failures; Sensors; SMJSs; strict LMIs; Time dependence; Time lag; time‐varying delays
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4230

Summary This paper deals with the problem of exponential H∞ filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an H∞ performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential H∞ performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods.