Further improved results on H_∞ filtering for discrete time-delay systems

This paper investigates the ^H∞ filtering problem for a class of discrete-time systems with time-varying delay. A model transformation is first applied by employing a two-term approximation for delayed state variables, which has a smaller approximation error than the other one-term approach. By using Scaled Small Gain Theorem and Lyapunov-Krasovskii functional approach, sufficient conditions are provided for the stability of the filtering error system with a prescribed ^H∞ performance level. In addition, sufficient conditions for the existence of the ^H∞ filters are established which are less conservative than the existing results in the literature. Finally, numerical examples are provided to illustrate effectiveness of the proposed filtering scheme.