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

  • Authors:

  • Frédéric Mazenc;Michael Malisoff;Zongli Lin

  • Affiliations:

  • Projet MERE INRIA-INRA, UMR Analyse des Systèmes et Biométrie INRA, 2 pl. Viala, 34060 Montpellier, France;Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, United States;Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, PO Box 400743, Charlottesville, VA 22904-4743, United States

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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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.