Nonsmooth Lur’e Dynamical Systems in Hilbert Spaces

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 invo...

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Bibliographic Details
Published inSet-valued and variational analysis Vol. 24; no. 1; pp. 13 - 35
Main Authors Adly, Samir, Hantoute, Abderrahim, Le, Ba Khiet
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2016
Springer
Subjects
Analysis
Mathematics
Mathematics and Statistics
Optimization
Optimization and Control
37J25
Maximal monotone operators
49J53
Nonsmooth Lur’e dynamical systems
37B25
Stability and robustness
46N10
Well-posedness
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Summary: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.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-015-0334-7