English

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}
}