Algebraic Test for Asymptotic Stability of Periodic Orbits for Polynomial Systems

2021/12/11 by Rafał Wiśniewski, Wisniewski, Rafał, Tom Nørgaard Jensen +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2112.05998

openalex publication_date 2021/12/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We will address the problem of determining the existence and asymptotic stability of a non-trivial periodic orbit in dynamical systems described by polynomial vector fields. To this end, we will lean upon the celebrated results of Borg, Olech and Hartman and newer results of Giesl, who all employ the concept of contraction for this purpose. Importantly, we formulate a numerically tractable algebraic test. The developed algorithm is illustrated in a numerical example.

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