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Further results on input-to-state stability for nonlinear systems with delayed feedbacks

Frédéric Mazenc 1 Michael Malisoff 2 Zongli Lin
1 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
2 LSU Mathematics - Department of Mathematics [Baton Rouge]
Abstract : We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed-loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-to-state stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for the original undelayed dynamics, which establishes that the closed-loop systems are input-to-state stable (ISS) with respect to actuator errors. We illustrate our results using a generalized system from identification theory and other examples.
Keywords : DELAYED SYSTEMS INPUT-TO-STATE STABILITY LYAPUNOV FUNCTION CONSTRUCTIONS SYSTEME DE CONTROLE NON LINEAIRE SYSTEME DIFFERE
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https://hal.inria.fr/hal-00857808
Contributor : Alain Rapaport Connect in order to contact the contributor
Submitted on : Wednesday, September 4, 2013 - 10:02:42 AM
Last modification on : Wednesday, February 10, 2021 - 3:35:13 AM

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Frédéric Mazenc, Michael Malisoff, Zongli Lin. Further results on input-to-state stability for nonlinear systems with delayed feedbacks. Automatica, Elsevier, 2008, 44 (9), pp.2415-2421. ⟨10.1016/j.automatica.2008.01.024⟩. ⟨hal-00857808⟩

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