Stability Analysis of Conewise Affine Dynamical Systems Using Conewise Linear Lyapunov Functions

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2 Scopus citations


This letter proposes computational algorithms for analyzing conewise affine dynamical systems, where every neighborhood of the origin contains an affine mode. These algorithms are based on conewise linear Lyapunov functions. To make such algorithms useful, we present an algorithm to automatically search over partitions defining these conewise Linear functions. This algorithm is sound, although we present a counter-example to its completeness. We show that this approach verifies stability of 2D and 3D examples of conewise affine dynamical systems, including combinations of the harmonic and nonsmooth oscillators.

Original languageEnglish
Article number9302672
Pages (from-to)2126-2131
Number of pages6
JournalIEEE Control Systems Letters
Issue number6
StatePublished - Dec 2021

Bibliographical note

Funding Information:
Manuscript received September 14, 2020; revised November 21, 2020; accepted December 6, 2020. Date of publication December 22, 2020; date of current version April 13, 2021. This work was supported by the Department of Mechanical Engineering at the University of Kentucky. Recommended by Senior Editor M. Arcak.

Publisher Copyright:
© 2017 IEEE.


  • Computational met23hods
  • Lyapunov methods
  • optimization
  • switched systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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