Reduced-order filter design of T-S fuzzy stochastic systems with time-varying delay

This paper focuses on the H∞ reduced-order filter design problem for discrete-time Takagi-Sugeno (T-S) fuzzy delayed systems with stochastic perturbation. Firstly, by using the reciprocally convex method and a novel fuzzy Lyapunov functional, the proposed basis-dependent condition is utilized to guarantee that the filtering error system is mean-square asymptotically stable with a pre-specified H∞ performance. Then, the corresponding solution of the reduced-order filter model is obtained, which can be transformed into a convex optimization problem by employing the convex linearization approach. Thus, it can be calculated by the standard optimization toolbox. Finally, the advantages and effectiveness of the proposed H∞ reduced-order filter design technique can be demonstrated by the simulation results, including the inverted pendulum system.