Global stabilization of nonlinear systems based on vector control lyapunov functions

Iasson Karafyllis, Zhong Ping Jiang

Research output: Contribution to journalArticlepeer-review

Abstract

This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: practically checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.

Original languageEnglish (US)
Article number6519314
Pages (from-to)2550-2562
Number of pages13
JournalIEEE Transactions on Automatic Control
Volume58
Issue number10
DOIs
StatePublished - 2013

Keywords

  • Feedback stabilization
  • Lyapunov functions
  • nonlinear systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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