Global stability of almost periodic solutions of monotone sweeping\n processes and their response to non-monotone perturbations

2017/04/20 by Mikhail Kamenskiĭ, Oleg Makarenkov, Kamenskii, Mikhail +4
Engineering · Mathematics · #34A60 #34C27 #34C29 #34D23 #Advanced Differential Equations and Dynamical Systems #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1704.06341

openalex publication_date 2017/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a theory which allows making qualitative conclusions about the\ndynamics of both monotone and non-monotone Moreau sweeping processes.\nSpecifically, we first prove that any sweeping processes with almost periodic\nmonotone right-hand-sides admits a globally exponentially stable almost\nperiodic solution. And then we describe the extent to which such a globally\nstable solution persists under non-monotone perturbations.\n

Related

• Global asymptotic stability of nonconvex sweeping processes
• Sweeping by a tame process
• Moreau-Yosida Regularization of Degenerate State-Dependent Sweeping Processes
• I. U. Bronshtein's Conjecture for Monotone Nonautonomous Dynamical Systems
• Poisson stable motions of monotone nonautonomous dynamical systems