New results on H_∞ filter design for nonlinear systems with time-delay through a T-S fuzzy model approach

Abstract

H _∞ filter design for nonlinear systems with time-delay via a T-S fuzzy model approach is investigated based on a piecewise analysis method. Two cases of time-varying delays are fully considered: one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. Based on a piecewise analysis method, the variation interval of the time delay is first divided into several subintervals, then the convexity property of the matrix inequality and the free weighting matrix method are fully used in this article. Some novel delay-dependent H _∞ filtering criteria are expressed as a set of linear matrix inequalities, which can lead to much less conservative analysis results. Finally, a numerical example is given to illustrate that the results in this article are more effective and less conservative than some existing ones.

Keywords:

• H _∞ filter
• linear matrix inequalities
• time delay
• fuzzy systems

Acknowledgements

The authors would like to acknowledge the Natural Science Foundation of China (NSFC) for its support under grant numbers 60834002, 60704024, 60904013 and 60774060.