A Qualitative Study for Nonsmooth Dynamical Systems
摘要
The present chapter studies the asymptotic behavior of nonsmooth dynamical systems determined by discontinuous differential equations. Thus, the chapter presents a study on decay rate and stability of solutions of discontinuous differential equations. The study carried out here uses the notions of Carathéodory and Krasovskii solutions for discontinuous differential equations. Then, using nonsmooth Lyapunov functions, we establish properties of decay rate and stability for nonsmooth dynamical systems. Moreover, we consider examples that illustrate the results established here.