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Conference Papers Year : 2017

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

Abstract

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.

Dates and versions

hal-01624048 , version 1 (26-10-2017)

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Cite

Sergio Waitman, Laurent Bako, Paolo Massioni, Gérard Scorletti, Vincent Fromion. Incremental stability of Lur’e systems through piecewise-affine approximations. 20th IFAC World Congress, International Federation of Automatic Control (IFAC). AUT., Jul 2017, Toulouse, France. pp.1673 - 1679, ⟨10.1016/j.ifacol.2017.08.491⟩. ⟨hal-01624048⟩
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