2017/08/26 by Andrii Mironchenko, Fabian Wirth, Mironchenko, Andrii +1
Engineering · #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1708.07953
openalex publication_date 2017/08/26 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We prove that input-to-state stability (ISS) of nonlinear systems over Banach\nspaces is equivalent to existence of a coercive Lipschitz continuous ISS\nLyapunov function for this system. For linear infinite-dimensional systems, we\nshow that ISS is equivalent to existence of a non-coercive ISS Lyapunov\nfunction and provide two simpler constructions of coercive and non-coercive ISS\nLyapunov functions for input-to-state stable linear systems.\n