LaSalle Invariance Principle for Ordinary Differential Equations and Applications

Abstract

The most popular method for studying stability of nonlinear systems is introduced by a Russian Mathematician named Alexander Mikhailovich Lyapunov. His work ”The General Problem of Motion Stability ” published in 1892 includes two methods: Linearization Method, and Direct Method. His work was then introduced by other scientists like Poincare and LaSalle . In chapter one of this work, we focused on the basic concepts of the ordinary differential equations. Also, we emphasized on relevant theorems in ordinary differential equations. In chapter two of this work, we study the existence and uniqueness of solutions of ordinary differential equations. Also, relevant theorems and concepts in ordinary differential equations was discussed in the chapter. In chapter three, we study the stability of an equilibrium point and linearization principle. Also, relevant theorems and concepts in stability of an equilibrium point and linearization principle was discussed in the chapter In chapter four, we study the various tools for determining stability of equilibrium points. In chapter five, we discussed various applications of Lyapunov theorem, and LaSalle’s invariance principle.