Well-posedness and nonsmooth Lyapunov pairs for state-dependent maximal monotone differential inclusions

2019/03/05 by Ba Khiet Le, Le, Ba Khiet · 1 citation
Computer Science · Engineering · Mathematics · #Contact Mechanics and Variational Inequalities #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC

paper · pdf · doi:10.48550/arxiv.1903.01815

arxiv created 2019/03/05 · openalex publication_date 2019/03/05 · arxiv updated 2019/03/06 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce for the first time a class of state-dependent maximal monotone differential inclusions. Then the existence and uniqueness of solutions are obtained by using an implicit discretization scheme and a kind of hypo-monotonicity assumption respectively. 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.

Citations

• On Properties of Differential Inclusions with Prox-regular Sets
• Lur'e dynamical systems with state-dependent set-valued feedback

Cited by

• On the Equilibria Computation of Set-Valued Lur'e Dynamical Systems

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