Observer design for systems with non small and unknown time-varying delay

Alexandre Seuret (1, 2, 3) , Thierry Floquet (4, 5) , Jean-Pierre Richard (4, 5) , Sarah K. Spurgeon (6)

1 Control and Instrumentation Research Group [Lancaster]
2 GIPSA-lab - Grenoble Images Parole Signal Automatique
3 NECS - Networked Controlled Systems
4 ALIEN - Algebra for Digital Identification and Estimation
5 SyNeR - Systèmes Non Linéaires et à Retards
6 Department of Electronics

This chapter deals with the design of observers for linear systems with unknown, time-varying, but bounded delays (on the state and on the input). In this work, the problem is solved for a class of systems by combining the unknown input observer approach with an adequate choice of a Lyapunov-Krasovskii functional for non small delay systems. 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 used to demonstrate the feasibility of the proposed solution.

Domaines: Automatique; Systèmes dynamiques [math.DS]

Alexandre Seuret, Thierry Floquet, Jean-Pierre Richard, Sarah K. Spurgeon. Observer design for systems with non small and unknown time-varying delay. J.J. Loiseau, W. Michiels, S.I. Niculescu, R. Sipahi. Topics in Time-Delay Systems: Analysis, Algorithms and Control, Springer Verlag, pp.233-242, 2009, LNCIS, Lecture Notes in Control and Information Sciences, 978-3-642-02896-0. ⟨10.1007/978-3-642-02897-7_20⟩. ⟨inria-00266457⟩