Maximal monotonicity and cyclic monotonicity arising in nonsmooth Lur'e dynamical systems

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• 作者：Samir Adly^a ; ^{samir.adly@unilim.fr} ; Abderrahim Hantoute^b ; ^{ahantoute@dim.uchile.cl} ; Ba Khiet Le^b ; ^{lkhiet@dim.uchile.cl}
• 关键词：Maximal monotonicity ; Maximal cyclic monotonicity ; Precomposition with linear operators ; Passivity condition ; Lur'e systems ; Differential inclusions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：691-706
• 全文大小：382 K
• 卷排序：448

文摘

We study a precomposition of a maximal monotone operator with linear mappings, which preserves the maximal monotonicity in the setting of reflexive Banach spaces. Instead of using the adjoint of such linear operators, as in the usual precomposition, we consider a more general situation involving operators which satisfy the so-called passivity condition. We also provide similar analysis for the preservation of the maximal cyclic monotonicity. These results are applied to derive existence results for nonsmooth Lur'e dynamical systems.