Extended design method of a Sliding Mode Observer for a class of linear uncertain time delay systems

In this paper, we propose an extension design method of a Sliding Mode Observer (SMO) for a class of linear uncertain time delay systems. This extension method is builds on the current SMO design methods for linear uncertain systems, but it gives a robust estimation of the states in spite of the presence of both uncertainty and time delay. We consider, in this work, a matched uncertainty and a constant time delay input and state. The basic idea in the design consists to combine the SMO concept with a Lyapunov-Krasovskï function which in numerically tractable via Linear Matrix Inequalities (LMIs) optimization. This design approach ensures the stability of the error estimation system. Besides, the dynamic properties of the observer are also analyzed. An illustrative example is given to show the validity and the applicability of the proposed approach.