Robust H∞$$ {H}_{\infty } $$ Filter Design for Uncertain 2‐D Singular Continuous Systems With State‐Varying Delay in Roesser Model

ABSTRACT

Robust performance analysis and robust 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 performance for all admissible uncertainties. This condition will be used later to design a robust filter. Finally, two numerical examples are provided to demonstrate the effectiveness and merits of the proposed approach.