H_∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays

Abstract

The problem of H _∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays is investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Furthermore, the derivative of the time-varying delay function can be larger than one. With partial knowledge of the jump rates of the Markov process, a new delay-range-dependent bounded real lemma for the solvability of the jump system is obtained based on the Lyapunov–Krasovskii functional, which is in terms of strict linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired H _∞ filter is given. Numerical examples are given to illustrate the effectiveness of the developed techniques.

Keywords:

• H _∞ control
• singular systems
• time-delay systems
• state estimation
• nonlinear filtering
• H _∞ filtering
• singular systems
• Markovian jumping systems

Acknowledgements

The authors would like to thank the reviewers for their very helpful comments and suggestions, which have improved the presentation of this article. The work of Yuanqing Xia was supported by the National Natural Science Foundation of China under Grant (60974011), Programme for New Century Excellent Talents in University of People's Republic of China (NCET-08-0047), the PhD Programmes of the Foundation of Ministry of Education of China (20091101110023), and the Programme for Changjiang Scholars and Innovative Research Team in University, and Beijing Municipal Natural Science Foundation (4102053), respectively.