Global Stabilization via Sampled-Data Output Feedback for a Class of Linearly Uncontrollable and Unobservable Systems

This note considers the problem of global stabilization using sampled-data output feedback for a class of nonlinear systems in the p-normal form which have uncontrollable and unobservable linearizations around the origin. A new sampled-data observer, which is featured with a special feedforward propagation structure, is constructed to estimate the unmeasurable states. The output feedback control law is obtained by discretizing the continuous-time homogeneous control law. Based on the trajectory estimation of the homogeneous system, a sampling period is determined to guarantee global asymptotic stability of the closed-loop system.