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

Sérgio Waitman; Paolo Massioni; Laurent Bako; Gérard Scorletti

doi:10.1016/j.automatica.2019.05.050

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 journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

83 Downloads (Pure)

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 language	English
Pages (from-to)	224-230
Number of pages	7
Journal	Automatica
Volume	107
Early online date	6 Jun 2019
DOIs	https://doi.org/10.1016/j.automatica.2019.05.050
Publication status	Published - 1 Sep 2019

Keywords

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

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10.1016/j.automatica.2019.05.050

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title = "Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions",

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.",

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AU - Waitman, Sérgio

AU - Massioni, Paolo

AU - Bako, Laurent

AU - Scorletti, Gérard

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Dissipativity

KW - Incremental gain

KW - Incremental stability

KW - Linear matrix inequalities

KW - Nonlinear systems

KW - Piecewise-affine systems

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DO - 10.1016/j.automatica.2019.05.050

M3 - Article (Academic Journal)

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VL - 107

SP - 224

EP - 230

JO - Automatica

JF - Automatica

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