Improved L₂-L_∞ filtering for stochastic time-delay systems

The L₂-L_∞ filtering problem for continuous-time polytopic uncertain stochastic timedelay systems is investigated. The main purpose is to design a full-order filter guaranteeing a prescribed L ₂-L_∞ attenuation level for the filtering error system. A simple alternative proof is given for an enhanced LMI (linear matrix inequality) representation of L₂-L_∞ performance. Based on the criterion which keeps Lyapunov matrices out of the products of system dynamic matrices, a sufficient condition for the existence of a robust estimator is formulated in terms of LMIs. The corresponding filter design is cast into a convex optimization problem. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.