Well-posedness and nonsmooth Lyapunov pairs for state-dependent maximal monotone differential inclusions. (2nd June 2020)

• Record Type: Journal Article
• Authors: Le, Ba Khiet
• Is Part Of: Optimization. Volume 69:Number 6(2020)
• Page Start: 1187
• Page End: 1217
• Publication Date: 2020-06-02
• Subjects: Differential inclusions -- maximal monotone operators -- state-dependent -- Lur'e systems -- sweeping processes; 49J40 -- 47J22 -- 49K40 -- 37B25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1686504
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we introduce a class of state-dependent maximal monotone differential inclusions. The existence and uniqueness of solutions are obtained by using an implicit discretization scheme and a kind of hypo-monotonicity assumption. In addition, a characterization for nonsmooth Lyapunov pairs associated with such systems is provided. Our result can be applied to study state-dependent sweeping processes and Lur'e dynamical systems. It is new even the involved maximal monotone operators depend only on the time.