Incremental stability of Lur'e systems through piecewise-affine approximations

Sérgio Waitman, Laurent Bako, Paolo Massioni, Gérard Scorletti, Vincent Fromion

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)


Lur'e-type nonlinear systems are virtually ubiquitous in applied control theory, which explains the great interest they have attracted throughout the years. The purpose of this paper is to propose conditions to assess incremental asymptotic stability of Lur'e systems that are less conservative than those obtained with the incremental circle criterion. The method is based on the approximation of the nonlinearity by a piecewise-affine function. The Lur'e system can then be rewritten as a so-called piecewise-affine Lur'e system, for which sufficient conditions for asymptotic incremental stability are provided. These conditions are expressed as linear matrix inequalities (LMIs) allowing the construction of a continuous piecewise-quadratic incremental Lyapunov function, which can be efficiently solved numerically. The results are illustrated with numerical examples.

Original languageEnglish
Pages (from-to)1673-1679
Number of pages7
Issue number1
Early online date18 Oct 2017
Publication statusE-pub ahead of print - 18 Oct 2017
Event20th IFAC World Congress - Toulouse, France
Duration: 9 Jul 201714 Jul 2017


  • incremental circle criterion
  • incremental stability
  • Lur'e systems
  • Lyapunov methods
  • piecewise-affine approximation
  • piecewise-affine systems


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