{"ID":6024144,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-09T20:50:17.003448696Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05640","arxiv_id":"2607.05640","title":"Input-to-State Stability Implications in Contraction Theory","abstract":"For nonlinear control systems on normed vector spaces, we characterize an incremental input-to-state stability (ISS) type property in which the overshoot constant multiplies both the initial-condition and the input terms. Working through the associated variational system, we show that two properties are equivalent: an ISS-type bound on the variational system, and the incremental ISS-type bound on the original system. We further establish the equivalence between an infinitesimal contraction condition, expressed through a Lyapunov-type function, and an incremental Lyapunov condition. Each of these equivalent conditions yields a necessary condition and a sufficient condition for the ISS-type bounds, differing only in the input Lipschitz constant of the vector field. When the overshoot constant equals one, the infinitesimal contraction condition reduces to the standard norm-based contraction conditions. We establish these implications under mere continuous differentiability of the vector field, and we illustrate the results through sensitivity matrices and Lyapunov characteristic exponents.","short_abstract":"For nonlinear control systems on normed vector spaces, we characterize an incremental input-to-state stability (ISS) type property in which the overshoot constant multiplies both the initial-condition and the input terms. Working through the associated variational system, we show that two properties are equivalent: an...","url_abs":"https://arxiv.org/abs/2607.05640","url_pdf":"https://arxiv.org/pdf/2607.05640v1","authors":"[\"Yu Kawano\",\"Francesco Bullo\"]","published":"2026-07-06T21:05:45Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}