Boundedness properties for time-varying nonlinear systems

A Liapunov theorem guaranteeing uniform boundedness and uniform ultimate bo undedness for a time-varying nonlinear system x(t) = f(x(t),t) has been est ablished. The study of uniform boundedness and uniform ultimate boundedness of particular classes of time-varying nonlinear systems x(t) = f (x(t),t) is reduced to the study of the corresponding time-invariant frozen systems x(t) = f(x(t),sigma) for all sigma is an element of R. This approach is ill ustrated for time-varying homogeneous systems with a positive order, for pa rticular classes of time-varying nonhomogeneous systems and for time-varyin g Lotka-Volterra equations.