Smooth feedback, global stabilization, and disturbance attenuation of nonlinear systems with uncontrollable linearization

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 g lobal stabilization and disturbance attenuation are solvable by smooth stat e 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 explici t construction of the smooth controllers. Several examples are presented to demonstrate the key features of the proposed nonlinear control schemes.