3 ASYMPTOTICAL STABILITY THEOREMS ON PARTIAL REGION WITH APPLICATIONS

For a long time, all stability theorems are concerned with the stabili ty of the zero solution of the differential equations of disturbed mot ion on the whole region of the neighborhood of the origin. But for var ious problems of dynamical systems, the stability is actually on parti al region. In other words, the traditional mathematical model is unmat ched with the dynamical reality and artificially sets too strict deman d which is unnecessary. In order to fill the gap between the tradition al mathematical model and dynamical reality of various systems, three asymptotical stability theorems on partial region are given and nine a pplications are presented.