{"ID":6536256,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10838","arxiv_id":"2607.10838","title":"On the Existence of Almost Periodic Solutions with Applications to Global Entrainment","abstract":"This paper provides two results that are useful in the study of the existence and the stability properties of almost periodic solutions for a given dynamical system. The obtained results are generalizations of recent results for periodic systems and are applied to the global entrainment problem in nonlinear time-invariant control systems. It is shown that local exponential stability for the unforced system and input-to-state stability with respect to small inputs can guarantee global entrainment to small almost periodic inputs. In this way, global entrainment is shown in Lotka-Volterra systems with a Volterra-Lyapunov stable interaction matrix. All results can be extended to the uniformly recurrent case.","short_abstract":"This paper provides two results that are useful in the study of the existence and the stability properties of almost periodic solutions for a given dynamical system. The obtained results are generalizations of recent results for periodic systems and are applied to the global entrainment problem in nonlinear time-invari...","url_abs":"https://arxiv.org/abs/2607.10838","url_pdf":"https://arxiv.org/pdf/2607.10838v1","authors":"[\"Iasson Karafyllis\",\"Miroslav Krstic\"]","published":"2026-07-12T17:03:07Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\",\"math.DS\",\"q-bio.PE\"]","methods":"[]","has_code":false}