Robust tracking for nonlinear systems represented by input-output models

This paper deals with designing an output feedback control for a class of single-input, single-output nonlinear systems that are represented by input-output models. The authors augment a series of m integrators at the input side, where m is the highest derivative of the input, and redefine the output and its derivatives to obtain an (n+m)-dimensional state model, where n is the order of the system. The purpose of the design is to force the output to asymptotically track a time-varying reference signal, while rejecting a time-varying disturbance input. The authors assume that exogenous signals are generated by a linear exosystem. Also the authors assume that the nonlinearities of the system will introduce only a finite number of harmonics of the original modes. This will enable one to identify the internal model as a linear servo-compensator. After augmenting the original system with the servo-compensator, the authors present conditions that will characterize a state feedback stabilizing control. Then, using a high gain observer, the authors show that the asymptotic properties achieved under state feedback control can be recovered