An extended sliding mode observer for a class of linear uncertain time-delay systems: Delay-dependent design method

For uncertain systems an extended Sliding Mode Observer (SMO) delay-dependent design method is presented in this paper. The considered uncertainty is bounded and the time delay is constant and affects simultaneously the input and state system. The basic design idea consists to combine the SMO concept with an adequate choice of a Lyapunov-Krasovskl functional. This design method is numerically tractable via Linear Matrix Inequalities (LMI) optimization. Besides, the dynamic properties of the observer are also analyzed and the reachability condition is satisfied. An illustrative example is given to show the validity and the applicability of the proposed approach.