Enhanced H _∞ filtering for continuous-time state-delayed systems

The H _∞ filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H _∞ attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality (LMI) representation of H _∞ performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a sufficient condition for the existence of robust estimators is formulated in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than some earlier results. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.