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

Alexandre Seuret (1) , Thierry Floquet (2, 3) , Jean-Pierre Richard (3, 4) , Sarah K. Spurgeon (5)

1 Control and Instrumentation Research Group [Lancaster]
2 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
3 ALIEN - Algebra for Digital Identification and Estimation
4 SyNeR - Systèmes Non Linéaires et à Retards
5 Department of Electronics

The 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.

Mots clés: Linear Matrix Inequalities; Sliding Mode Observer; Time-Delay Systems; Unknown Delay; Linear Matrix Inequalities.

Domaines: Automatique / Robotique

Alexandre Seuret, Thierry Floquet, Jean-Pierre Richard, Sarah K. Spurgeon. A sliding mode observer for linear systems with unknown time-varying delay. Automatic Control Conference, Jul 2007, New York City,, United States. pp.4558 - 4563, ⟨10.1109/ACC.2007.4282449⟩. ⟨hal-00385904⟩