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

Frédéric F. Mazenc (1, 2) , Michael Malisoff (3) , Zongli Lin (4)

1 ASB - Analyse des Systèmes et Biométrie
2 MERE - Water Resource Modeling
3 Department of mathematics
4 University of Virginia

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.

Mots clés: DELAYED SYSTEMS; INPUT-TO-STATE STABILITY; LYAPUNOV FUNCTION CONSTRUCTIONS; SYSTEME DIFFERE

Mots clés: SYSTEME DE CONTROLE NON LINEAIRE

Domaines: Automatique

Frédéric F. Mazenc, Michael Malisoff, Zongli Lin. Further results on input-to-state stability for nonlinear systems with delayed feedbacks. American control conference, Jul 2007, New-York, United States. ⟨10.1016/j.automatica.2008.01.024⟩. ⟨hal-02823563⟩