The Analysis Of Relative Stability For Nonlinear Differential Systems

Relative stability investigates the relationship between the solutions of two systems, andthis kind of problem has a fundamental role for the study of the system’s synchronization. Fromthe existing results, we know that whether for adaptive control, tracking control, or the mostpopular research field- chaos synchronization control, the relative stability is the necessarytheoretical basis. But so far, only a few literatures introduced the concept of relative stability.The general theory and method of relative stability have not formed.In this paper, we studied the relative stability criteria for classes of nonlinear differentialsystems by using Lyapunov functions method together with comparison principle. The maincontent of this paper consists of four parts. In part one, we investigated the equi-integrally ??0-relative stability of two different differential systems. In part two, we introduced the relative(?0, ?, ??0)-stability for two nonlinear differential systems by employing Lyapunov function,where the comparison system is upper quasi-monotone non-decreasing. In part three, we de-voted to discuss the relatively integral stability in terms of two measures for two differentialsystems with “maxima” by employing Lyapunov functions, Razumikhin method and compar-ison principle. An example is obtained to illustrate the main result. In part four, the relativelypractical stability and relatively ??0-practical stability in terms of two measures for two differ-ential systems with “maxima” were obtained. An example is given to illustrate the main result.