Geometry of V-functions and the Liapunov stability theory

Geometric properties of V-functions are studied and the application of such functions to nominal equations of a dynamical system is considered. A theorem is proved that provides a framework for quantitative design and investigation of motions. The results allow direct control applications. The application is made to the perturbation equation where classical Liapunov theorems follow as a special case whereby the investigation of locally unstable but ??-stable systems is made possible. An example is presented.