Sampled-data feedback practical semi-global controllability and stabilization for time-varying systems

Abstract

We deal with the problems of the closed-loop controllability and stabilization for time-varying systems whose dynamics are in general unbounded with respect to time. It is shown that a general notion of global asymptotic controllability, being in general, non-uniform with respect to initial values of time, implies existence of a family of continuous control Lyapunov functions, and this enables the establishment of practical semi-global closed-loop controllability by means of a sampled-data time-varying feedback. Moreover, the usual concept of global asymptotic controllability, being uniform with respect to the initial values of time, implies practical semi-global stabilization by sampled-data feedback. The work is a continuation of a recent paper of the author in the same journal and extends Krichman's (2000) result relying practical stabilization of time-varying systems with bounded in time dynamics.