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arXiv · 2510.14057

Lyapunov methods for input-to-state stability of time-varying evolution equations

Rahma Heni·Andrii Mironchenko·Fabian Wirth·Hanen Damak·Mohamed Ali Hammami
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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.

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Rahma Heni, Andrii Mironchenko, Fabian Wirth, Hanen Damak, Mohamed Ali Hammami. 2025-10-15. Lyapunov methods for input-to-state stability of time-varying evolution equations. https://arxiv.org/abs/2510.14057

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