Abstract
The results of the paper concern a broad family of time-varying nonlinear systems with
differentiable motions. The solutions are established in a form of the necessary and sufficient conditions
for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system
Lyapunov function and 3) for an accurate single determination of the (uniform) asymptotic stability
domain. They permit arbitrary selection of a function p(⋅) from a defined functional family to
determine a Lyapunov function v(⋅), [v(⋅)], by solving v′(⋅)=−p(⋅) {or equivalently,
v′(⋅)=−p(⋅)[1−v(⋅)]}, respectively. Illstrative examples are worked out.