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Nonsmooth Lur’e Dynamical Systems in Hilbert Spaces

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Abstract

In this paper, we study the well-posedness and stability analysis of set-valued Lur’e dynamical systems in infinite-dimensional Hilbert spaces. The existence and uniqueness results are established under the so-called passivity condition. Our approach uses a regularization procedure for the term involving the maximal monotone operator. The Lyapunov stability as well as the invariance properties are considered in detail. In addition, we give some sufficient conditions ensuring the robust stability of the system in finite-dimensional spaces. The theoretical developments are illustrated by means of two examples dealing with nonregular electrical circuits and an other one in partial differential equations. Our methodology is based on tools from set-valued and variational analysis.

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Authors and Affiliations

  1. XLIM UMR-CNRS 7252, Université de Limoges, 87060, Limoges, France

    Samir Adly

  2. Centro de Modelamiento Matemático (CMM), Universidad de Chile, Santiago, Chile

    Abderrahim Hantoute & Ba Khiet Le

Authors
  1. Samir Adly
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  2. Abderrahim Hantoute
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  3. Ba Khiet Le
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Correspondence to Samir Adly.

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Dedicated to professor Lionel Thibault on the occasion of his birthday.

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Adly, S., Hantoute, A. & Le, B.K. Nonsmooth Lur’e Dynamical Systems in Hilbert Spaces. Set-Valued Var. Anal 24, 13–35 (2016). https://doi.org/10.1007/s11228-015-0334-7

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  • DOI: https://doi.org/10.1007/s11228-015-0334-7

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