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

Authors:
Xiuming Yao;Ligang Wu;Wei Xing Zheng;Changhong Wang
Affiliations:
Space Control and Inertial Technology Research Centre, Harbin Institute of Technology, Harbin, 150001, P.R. China,School of Control Science and Engineering, North China Electric Power University, ...;Space Control and Inertial Technology Research Centre, Harbin Institute of Technology, Harbin, 150001, P.R. China;School of Computing and Mathematics, University of Western Sydney, Penrith South DC, NSW 1797, Australia;Space Control and Inertial Technology Research Centre, Harbin Institute of Technology, Harbin, 150001, P.R. China
Venue:
International Journal of Systems Science
Year:
2011

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Abstract

This article investigates the problem of robust H∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Ito-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.