Stabilization of driftless nonlinear systems via time-varying state feedback

Abstract

Sufficient conditions are presented under which a general nonlinear system without drift is globally asymptotically stabilizable by time-varying state feedback. A novel approach is developed for the design of a time-varying smooth state feedback controller. The controller is explicitly constructed by using the bounded state feedback strategy combined with Lyapunov technique as well as lossless systems theory. This work incorporates earlier global stabilization results for controllable affine systems without drift, which are known not to be smoothly stabilizable via time-invariant state feedback.