The Study Of A Class Of Strict Practical Stability Of Nonlinear Differential System

Strict stability is different from Lyapunov stability and can provide more accurate information about the solutions in practical problem. In this paper, it is analysed that strict stability and strict prac-tical stability of nonlinear differential systems relative to initial time difference by using differential inequalities technique. In chapter1, some fundamental theories of stability of nonlinear differen-tial equation are given. In chapter2, we develop the concepts of stability of nonlinear differential equations with initial time difference to strict stability of nonlinear differential equations with initial time difference. In this chapter, we provide several criteria of strict stability of nonlinear differen-tial systems relative to initial time difference. A comparison principle with initial time unchanged is presented. By employing the presented comparison principle, we obtain a new strict stability criteria of nonlinear differential equations with initial time difference. In chapter3, we develop the concepts of practical stability of nonlinear differential equations with initial time difference to strict practical stability of nonlinear differential equations with initial time difference. Several strict practical sta-bility criteria and a comparison principle of nonlinear differential equations with solutions starting with different initial times are presented. The novel results enrich the theory of practical stability of nonlinear differential equations relative to initial time difference.