Input-Power-to-State Stability of Time-Varying Systems
Abstract
When the state of a system may remain bounded even if both the input amplitude and energy are unbounded, then the state bounds given by the standard input-to-state stability (ISS) and integral-ISS (iISS) properties may provide no useful information. This paper considers an ISS-related concept suitable in such a case: input-power-to-state stability (IPSS). Necessary and sufficient conditions for IPSS are developed for time-varying systems under very mild assumptions on the dynamics. More precisely, it is shown that (a) the existence of a dissipation-form ISS-Lyapunov function implies IPSS, but not necessarily that of an implication-form one, (b) iISS with exponential class- function implies IPSS, and (c) ISS and stronger assumptions on the dynamics imply the existence of a dissipation-form ISS-Lyapunov function and hence IPSS. The latter result is based on a converse Lyapunov theorem for time-varying systems whose dynamics (i.e. state derivative) is not necessarily continuous with respect to time.
Keywords
Cite
@article{arxiv.2505.24805,
title = {Input-Power-to-State Stability of Time-Varying Systems},
author = {Hernan Haimovich and Shenyu Liu and Antonio Russo and Jose L. Mancilla-Aguilar},
journal= {arXiv preprint arXiv:2505.24805},
year = {2025}
}
Comments
Submitted to Automatica