Consistent Lyapunov methodology, time-varying nonlinear systems and sets (Q1961254)

The main difficulty in the application of the classical Lyapunov method is to find an appropriate Lyapunov function. Earlier, the author developed a method for time-invariant systems considering a functional family that could be used to generate an appropriate Lyapunov function [\textit{R. Bouyekhf} and the author, Nonlinear Dyn. 18, No. 2, 107-127 (1999; Zbl 0939.93029)]. It was called the consistent Lyapunov methodology. This methodology is extended to time-varying nonlinear systems with differentiable motions to guarantee uniform asymptotic stability of invariant sets of such systems.