Lyapunov Functions for Switched Linear Systems: Proof of Convergence for an LP Computational Approach

Sigurdur Hafstein*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A recent approach uses linear programming (LP) to compute continuous and piecewise affine (CPA) Lyapunov functions for arbitrary switched linear systems. Such a Lyapunov function is a common Lyapunov function (CLF) for all the respective linear subsystems and asserts the exponential stability of the equilibrium at the origin for the switched system. In this letter, we prove that this LP approach is constructive, i.e., that it succeeds in computing a Lyapunov function for the switched system, whenever the origin is exponentially stable.

Original languageEnglish
Pages (from-to)3283-3288
Number of pages6
JournalIEEE Control Systems Letters
Volume7
DOIs
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Other keywords

  • Common Lyapunov function
  • linear programming
  • linear systems
  • switched systems

Fingerprint

Dive into the research topics of 'Lyapunov Functions for Switched Linear Systems: Proof of Convergence for an LP Computational Approach'. Together they form a unique fingerprint.

Cite this