Sufficient conditions for closed-loop asymptotic controllability and stabilization by smooth time-varying feedback integrator

For general finite-dimensional time-varying nonlinear systems we derive sufficient conditions for closed-loop asymptotic controllability and asymptotic stabilization by means of a smooth ordinary time-varying feedback integrator. The main hypotheses are based on the existence of an almost smooth time-varying control Lyapunov function. The corresponding results generalize earlier works in the literature concerning feedback stabilization for nonlinear autonomous systems that in general cannot be stabilized by continuous time-varying state feedback.