The Converse Theorem of Lyapunov Exponential Stability Theorem

Abstract

The dynamical behavior for nonautonomous is complicated.So, even if some basic concepts in the dynamical theory for nonautonomous systems are still undergoing investigations and need to be further developed. And Lyapunov functions play an important role in the study of the stability theory and control theory. In the view of the use of Lyapunov method, this paper is concerned with a converse theorem of Lyapunov exponential stability theorem. First, we show the content of the theorem, and then the proof is given.