Filtering for a class of discrete-time systems with time-delays via delta operator approach

Abstract

In this article, a robust H _∞ filtering problem for a class of norm-bounded uncertain discrete-time systems with time delays is investigated using delta operator approach. Based on Lyapunov–Krasovskii functional in delta domain, a new delay-dependent sufficient condition for the solvability of this problem is presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired delta operator H _∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into a delta operator systems framework. A numerical example is given to illustrate the effectiveness of the developed techniques.

Keywords:

• delta operator systems
• H _∞ filtering
• robust filtering
• time delays
• LMIs
• norm-bounded uncertainties
• asymptotic stability
• robust control
• state-space models

Acknowledgements

The authors would like to thank the reviewers for their very helpful comments and suggestions which have improved the quality of the paper. The Work of Yuanqing Xia was supported by the National Natural Science Foundation of China under Grant 60504020, Program for New Century Excellent Talents in University of People's Republic of China, NCET-08-0047, Fund of Beijing Institute of Technology 2008YS0104 and Program for Changjiang Scholars and Innovative Research Team in University, respectively.