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Linear Singular Continuous Time-varying Delay Equations: Stability and Filtering via LMI Approach
Vu Ngoc Phat
,
Nguyen Truong Thanh
Abstract
In this paper, we propose an LMI-based approach to study stability and $H_\infty$ 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 $H_\infty$ 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.