ROBUST STABILIZATION OF FEEDBACK LINEARIZABLE TIME-VARYING UNCERTAIN NONLINEAR-SYSTEMS

We consider single-input nonlinear systems with unknown unmodelled time-varying parameters or disturbances whose bounds are known. Assuming that the undisturbed system is globally feedback linearizable and that a triangularity condition holds for the uncertain terms we design a robust global stabilizing state feedback control. Disturbances are not required to enter linearly in the state equations. When they do enter linearly, the stabilization problem can be solved without knowing bounds on disturbances by using a self-tuning version of the robust control. In particular, any linear system in controller canonical form perturbed by unknown global Lipschitz nonlinearities satisfying triangularity conditions is shown to be globally stabilizable by a fixed dynamic state feedback compensator whose order equals the state space dimensions.