On hyperexponential stabilization of double integrator in continuous and discrete time

Abstract

A time-varying state feedback is presented that guarantees stability with hyperexponential rate of convergence of all trajectories to the origin for a double integrator system. It is shown that this convergence property is uniform with respect to matched bounded external disturbances. An implicit time-discretization scheme of the closed-loop system is given, which preserves all main properties of the continuous-time counterpart, and in addition has bounded errors with respect to the measurement noises. Based on this discretization, for sampled-and-hold implementation, a modified linear time-varying state feedback is proposed providing an accelerated rate of convergence to the continuous-time plant. The efficiency of the suggested control is illustrated through numeric experiments.