Lyapunov methods for input-to-state stability of time-varying evolution equations
Optimization and Control
2025-10-17 v1
Abstract
We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In particular, input-to-state stability of linear time-varying control systems in Hilbert spaces with bounded input operators is discussed. Methods for the construction of non-coercive LISS/iISS Lyapunov functions are presented for a certain class of time-varying semi-linear evolution equations. Two examples are given to illustrate the effectiveness of the results.
Cite
@article{arxiv.2510.14057,
title = {Lyapunov methods for input-to-state stability of time-varying evolution equations},
author = {Rahma Heni and Andrii Mironchenko and Fabian Wirth and Hanen Damak and Mohamed Ali Hammami},
journal= {arXiv preprint arXiv:2510.14057},
year = {2025}
}
Comments
35 pages