New results on H∞ filtering for fuzzy systems with interval time-varying delays

This paper investigates the problem of H∞ filtering for continuous Takagi–Sugeno (T–S) fuzzy systems with an interval time-varying delay in the state. Based on the delay partitioning idea, a new approach is proposed for solving this problem, which can achieve much less conservative feasibility conditions. The attention is focused on the design of an H∞ filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the H∞ attenuation level from disturbance to estimation error is below a prescribed scalar. The constructed Lyapunov–Krasovskii functional, by applying the delay partitioning method, can potentially guarantee the obtained delay-dependent conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. Finally, an example is illustrated to show the reduction in conservatism of the proposed filter design method.