{"ID":2855393,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.14057","arxiv_id":"2510.14057","title":"Lyapunov methods for input-to-state stability of time-varying evolution equations","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.","short_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 Hilber...","url_abs":"https://arxiv.org/abs/2510.14057","url_pdf":"https://arxiv.org/pdf/2510.14057v1","authors":"[\"Rahma Heni\",\"Andrii Mironchenko\",\"Fabian Wirth\",\"Hanen Damak\",\"Mohamed Ali Hammami\"]","published":"2025-10-15T19:54:04Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}