Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

Sérgio Waitman*, Paolo Massioni, Laurent Bako, Gérard Scorletti

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

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Abstract

This paper concerns the incremental L2-gain stability of piecewise-affine (PWA) systems. We propose sufficient conditions derived from dissipativity theory to compute an upper bound on the incremental L2-gain. This is achieved by constructing piecewise-polynomial storage functions through the use of sum of squares (SOS) relaxations. The constraints are expressed as linear matrix inequalities (LMIs), which can be solved numerically in an efficient way. The proposed conditions are verified to be less conservative than previous results found in the literature by means of a numerical example.

Original languageEnglish
Pages (from-to)224-230
Number of pages7
JournalAutomatica
Volume107
Early online date6 Jun 2019
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • Dissipativity
  • Incremental gain
  • Incremental stability
  • Linear matrix inequalities
  • Nonlinear systems
  • Piecewise-affine systems

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