2015/07/20 by Jun Liu, Andrew R. Teel, Liu, Jun +1
Engineering · Medicine · #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1507.05648
openalex publication_date 2015/07/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals. Examples are provided to illustrate these conditions.