H∞ performance based filtering for time-varying systems via T-S fuzzy modelling

This paper considers H∞ reduced-order filtering problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delay in its state. Firstly, Based on the reciprocally convex methods and a novel fuzzy Lyapunov functional, the proposed basis-dependent condition is utilized to ensure that the resulted error system is asymptotically stable with a prescribed H∞ performance and reduce the conservativeness. Then, By utilization of the convex linearization technique, the sufficient condition of reduced-order filter design can be casted into linear matrix inequality constraints. Finally, the desired filters can be obtained based on standard numerical algorithms.