Linear Singular Continuous Time-varying Delay Equations: Stability and Filtering via LMI Approach

In this paper, we propose an LMI-based approach to study stability and \(H_\infty \) $H_{\infty }$ filtering for linear singular continuous equations with time-varying delay. Particularly, the delay pattern is quite general and includes non-differentiable time-varying delay. First, new delay-dependent sufficient conditions for the admissibility of the equation are extended to the time-varying delay case. Then, we propose a design of \(H_\infty \) $H_{\infty }$ filters via feasibility problem involving linear matrix inequalities, which can be solved by the standard numerical algorithm. The proposed result is demonstrated through an example and simulations.