Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

• Published in: International journal of systems science Vol. 42; no. 7; pp. 1219 - 1230
• Main Authors: Yao, Xiuming, Wu, Ligang, Zheng, Wei Xing, Wang, Changhong
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.07.2011; Taylor & Francis
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; filtering; Markovian jump systems; Modelling and identification; stochastic systems; time-varying delay; uncertain transition probability; Markov process; Itô equation; Disturbance rejection; H∞ filtering; Stochastic integral; Transition matrix; Time varying system; Transition system; Uncertain system; Linear matrix inequality; Transition probability; stochastic systems; Markovian jump systems; Jump process; Delay time; Delayed time; time-varying delay; Existence condition; Markovian system; Probabilistic approach; H infinite control; Delay system; Temporal constraint; Filter; Jumping; Non deterministic system; uncertain transition probability; Lyapunov function
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207720903513350

This article investigates the problem of robust ℋ ∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Itô-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an ℋ ∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed ℋ ∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov-Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.