A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay

摘要

In this paper, the problem of $ell_{2}$- $ell_{infty }$ filtering for a class of discrete-time Takagi–Sugeno (T–S) fuzzy time-varying delay systems is studied. Our attention is focused on the design of full- and reduced-order filters that guarantee the filtering error system to be asymptotically stable with a prescribed $mathscr{H}_{infty }$ performance. Sufficient conditions for the obtained filtering error system are proposed by applying an input–output approach and a two-term approximation method, which is employed to approximate the time-varying delay. The corresponding full- and reduced-order filter design is cast into a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, simulation examples are provided to illustrate the effectiveness of the proposed approaches.