Further improvement on H∞ filtering for time-delayed systems

This paper addresses the H_∞ filtering problem for time-delay systems with parameter uncertainty in a given convex polytope. To design a filter guaranteeing the asymptotic stability of the system with a prescribed H_∞ performance level, a model transformation is first applied employing a two-term approximation for delayed state variables, which has a smaller approximation error than the error given by a one-term approach. Based on Scaled Small Gain (SSG) Theorem and the proposed Lyapunov-Krasovskii Functional (LKF), the stability and the H_∞ performance of the system are analyzed. The resulting conditions are developed for an uncertain system, and the corresponding H_∞ filtering design scheme with less conservatism is proposed. Finally, two examples are presented to show effectiveness of the filtering scheme.