Control design with guaranteed ultimate bound for feedback linearizable systems

For a class of perturbed feedback linearizable nonlinear systems, we consider the computation and assignment of prescribed ultimate bounds on the system states. We employ a recently proposed componentwise bound computation procedure, which directly takes into account both the system and perturbation structures by performing componentwise analysis. We first derive sufficient conditions to ensure that the trajectories originating from initial conditions in an appropriate set are ultimately bounded. Secondly, and most importantly, for state-feedback-linearizable nonlinear systems with matched perturbations, we provide a systematic design procedure to compute a state feedback control that ensures a prescribed ultimate bound for the closed-loop system states. The procedure combines nonlinear state-feedback-linearizing control with a state-feedback matrix computed via an eigenstructure assignment method previously reported by the authors. A simulation example illustrates the simplicity and systematicity of the proposed design method.