Extension of the solution properties and stability concepts in the nonlinear dynamical systems with using measure functions

Abstract

The Lyapunov stability theory has been a well-known and powerful method for justifying the solution property and also stability analysis of an equilibrium point in the nonlinear systems. The stability notions may usually be expressed in terms of some norm functions in the conventional Lyapunov stability theory. In this paper, the boundedness and stability concepts would been investigated within a defined set instead of the equilibrium point. Then, based on the measure functions concept, the boundedness and also stability properties of the solution will be extended to develop a modified stability theory in the nonlinear systems.