Converse Theorems of the Principal Lyapunov Results for Partial Stability of General Dynamical Systems on Metric Spaces

Abstract

We present converse theorems for the Principal Lyapunov Results concerning partial stability properties of general dynamical systems defined on metric spaces. We consider the general case of partial stability with respect to disturbances in all of the initial state variables $x_0 = (y_0, z_0)$ as well as the case of $y$-stability under arbitrary $z$-perturbations.