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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 Spurgeon 5
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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.
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Alexandre Seuret, Thierry Floquet, Jean-Pierre Richard, Sarah 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⟩

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