2013/10/10 by Chaitanya Murti, Murti, Chaitanya, Matthew M. Peet +2
Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #math.OC
paper · pdf · doi:10.48550/arxiv.1310.2701
arxiv created 2013/10/10 · openalex publication_date 2013/10/10 · arxiv updated 2013/10/11 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided.