Three asymptotical stability theorems on partial region with applications

Abstract

For a long time, all stability theorems are concerned with the stability of the zero solution of the differential equations of disturbed motion on the whole region of the neighborhood of the origin. But for various problems of dynamical systems, the stability is actually on partial region. In other words, the traditional mathematical model is unmatched with the dynamical reality and artificially sets too strict demand which is unnecessary. In order to fill the gap between the traditional mathematical model and dynamical reality of various systems, three asymptotical stability theorems on partial region are given and nine applications are presented.