H∞ filtering for sampled-data fuzzy systems

Takagi-Sugeno fuzzy system can describe a wide class of nonlinear systems, and is widely used in many engineering fields. Recently, system analysis and control design for nonlinear systems based fuzzy system approach have been active. This paper is concerned with H_infin filtering for sampled-data fuzzy systems. The system is usually modelled as a continuous-time fuzzy system, while the observation is taken at discrete instants. First it is shown that the error system which comes from an original fuzzy system and a sampled-data filter becomes a system with time-varying delay. Sufficient conditions for the error system to achieve the stability with H_infin disturbance attenuation are given in terms of linear matrix inequalities(LMIs). We derive such conditions via output delay system approach under the assumption that sampling-time is not greater than some prescribed number. Based on such conditions, we propose an H_infin sampled-data filter design for a fuzzy system. Numerical examples are given to illustrate our H_infin sampled-data filtering.