Smooth Feedback, Global Stabilization, and Disturbance Attenuation of Nonlinear Systems with Uncontrollable Linearization

Abstract

Problems of global asymptotic stabilization and disturbance attenuation are addressed for a class of highly nonlinear systems that are comprised of a lower dimensional zero-dynamics subsystem and a chain of power integrators perturbed by a nontriangular vector field. It is shown in this paper that global stabilization and disturbance attenuation are solvable by smooth state feedback if one takes full advantage of the characteristics of the system in the feedback design to dominate the nonlinearity rather than to cancel it. A systematic design procedure which is based upon, but generalizes, the recent technique of adding a power integrator is developed for the explicit construction of the smooth controllers. Several examples are presented to demonstrate the key features of the proposed nonlinear control schemes.