H ∞ $H_{\infty}$ Fuzzy filtering for nonlinear singular systems with time-varying delay

This paper considers the H-infinity fuzzy filtering problem for continuous-time nonlinear singular systems with time-varying delay through the T-S fuzzy model approach. Firstly, by combining a reciprocally convex combination lemma and the fuzzy Lyapunov-Krasovskii function method, a new bounded real lemma (BRL) is proposed such that the resultant closed-loop systems are admissible and satisfy the prescribed H-infinity disturbance attenuation. Then, by using the matrix decoupling technique, we translate the BRL into another form, which separates the coefficient matrices of systems and Lyapunov matrices. On the basis of such a new form of BRL, the fuzzy filter design problem is solved by checking the feasibility of a series of linear matrix inequalities (LMIs), and the filter gains can also be provided explicitly. Numerical examples are presented to show the reduction of the conservativeness compared to some published results in the literature.