Robust H∞ filtering for sampled-data fuzzy systems

This paper is concerned with robust H∞ filtering for Takagi–Sugeno sampled-data fuzzy systems with uncertain parameters. 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. The system is usually modelled as a continuous-time system, while in practical situations the observation is taken at discrete instants. Such an observation can be represented as a delayed signal. First it is shown that the error system which stems 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 robust stability with H∞ 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 a robust H∞ sampled-data filter design for a fuzzy system. We consider two different cases for the premise variables in our filter design. Numerical examples are given to illustrate our robust H∞ sampled-data filtering.