Robust H∞ Filter Design for Uncertain 2-D Singular Continuous Systems With State-Varying Delay in Roesser Model

Abstract

Robust $H_{\infty }$ performance analysis and robust $H_{\infty }$ filtering design are considered here for uncertain two-dimensional (2-D) singular continuous state-varying delay systems with norm-bounded parameter uncertainties. Based on the augmented Lyapunov-Krasovskii functional (LKF) with triple integral terms and the use of the Wirtinger inequality combined with an improved reciprocally convex approach, a new sufficient admissibility condition is obtained, which guarantees that the 2-D singular filtering error is regular, causal, and stable and satisfies the $H_{\infty }$ performance for all admissible uncertainties. This condition will be used later to design a robust $H_{\infty }$ filter. Finally, two numerical examples are provided to demonstrate the effectiveness and merits of the proposed approach.