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

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 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.

Keywords:

• Markovian jump systems
• stochastic systems
• uncertain transition probability
• ℋ_∞ filtering
• time-varying delay

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 60804002, the Natural Science Foundation of Heilongjiang Province of China (QC2009C58), Programme for New Century Excellent Talents in University, 973 Project (2009CB320600), the Chinese Post-doctor Science Foundation (20090460892), a research grant from the Australian Research Council and a research grant from the University of Western Sydney, Australia.