Improved stability and H∞ performance criteria for linear systems with interval time-varying delays via three terms approximation

This paper investigates the problem of delay dependent stability and H_∞ performance for a class of linear systems with interval time-varying delay. A new model transformation is first proposed by employing a three-terms approximation of delayed state variables, for a better approximation of delayed state. By using scaled small gain theorem and a simple Lyapunov–Krasovskii functional, new stability and H_∞ performance criteria are proposed in terms of linear matrix inequalities, which can be easily solved by using standard numerical packages. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.     

H ∞ Filtering of Two-Dimensional T-S Fuzzy Systems

The H _∞ filtering problem for two-dimensional Takagi–Sugeno fuzzy systems described by the Fornasini–Marchesini (FM) model is studied. Attention is focused on the design of an H _∞ fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H _∞ performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H _∞ fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism.