A sliding mode observer for linear systems with unknown time-varying delay

International audienceThe design of observers for linear systems with unknown, time-varying, bounded delays (on the state and on the input) still constitutes an open problem. In this paper, we show how to solve it for a class of systems by combining the sliding mode observer approach with an adequate choice of a Lyapunov-Krasovskii functional. This result provides workable conditions in terms of rank assumptions and LMI conditions. The dynamic properties of the observer are also analyzed. A 4th-order example is proposed to study the feasibility