Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces
Optimization and Control
2017-08-29 v1 Analysis of PDEs
Dynamical Systems
Abstract
We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that ISS is equivalent to existence of a non-coercive ISS Lyapunov function and provide two simpler constructions of coercive and non-coercive ISS Lyapunov functions for input-to-state stable linear systems.
Keywords
Cite
@article{arxiv.1708.07953,
title = {Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces},
author = {Andrii Mironchenko and Fabian Wirth},
journal= {arXiv preprint arXiv:1708.07953},
year = {2017}
}