The General Stability – Like Concepts for Differential and Control System

Abstract

Theorems corresponding to the concepts of stability discussed in the works under reference should follow the general pattern of the direct method of Lyapunov. Theorems proved for such stability contain, as special cases results on - (i) stability for the origin, (ii) stability with respect to some components, (iii) stability of a set A, (iv) stability of a set A (t), (v) stability of conditional invariant set B relative to A, (vi) Stability of asymptotic invariant set A and (vii) stability of conditional asymptotic invariant set B relative to A. It is shown that our results on the stability properties can be extended to cover control systems with the set of controls compact in Rm.