Observer design for nonlinear systems under unknown time-varying delays

Malek Ghanes 1 J. Deleon 2 Jean-Pierre Barbot 3, 1
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both state and input, still constitutes an open problem. In this paper, we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a Lyapunov-Krasovskii functional suitable choice. Sufficient conditions are provided to prove the practical stability of the observer. It is shown that the observation error is bounded and depends on the size of two parameters: the known upper bound delay of the unknown time-varying function delay and the instantaneous state dynamic variation. Furthermore, for the particular case of constant known time delay, the convergence of the proposed observer becomes exponential. The feasibility of the proposed strategy is illustrated by a numerical example.
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IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2013, to appear
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Malek Ghanes, J. Deleon, Jean-Pierre Barbot. Observer design for nonlinear systems under unknown time-varying delays. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2013, to appear. 〈hal-00749682〉

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