Stability and Stabilization of Nonlinear Dynamical Systems

Abstract

In the analysis and control of linear and non linear systems,the most important thing is to study stability,because an unstable system is usually useless.The objective of this memoir is to present the lyapunov method,and analyze the stability of non linear systems.This memoir is concerned with the asymptotic stability analysis of linear time-varying(LTV)systems.With the help of the notion of stable functions,some the differential Lyapunovin equalities based on necessary and sufficient conditions are derived for testing the asymptotic stability,exponential stability,and input-to-statest ability of generalL TV systems