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arXiv · 2505.24805

Input-Power-to-State Stability of Time-Varying Systems

Hernan Haimovich·Shenyu Liu·Antonio Russo·Jose L. Mancilla-Aguilar
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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-$\KL$ 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.

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Hernan Haimovich, Shenyu Liu, Antonio Russo, Jose L. Mancilla-Aguilar. 2025-05-30. Input-Power-to-State Stability of Time-Varying Systems. https://arxiv.org/abs/2505.24805

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