New Sliding Mode Observer for a class of linear uncertain time-varying delay systems: delay-dependent design method

In this paper, we propose a new Sliding Mode Observer (SMO) for uncertain time-varying delay-dependent systems that builds on the available methods used for uncertain and delayed systems. In meantime, the considered uncertainty is bounded and the time-delay is varying and affects the state system. The basic design idea consists to combine the SMO concept with an adequate choice of a Lyapunov-Krasovski 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.