Performance Limitation in Output Regulation of an Uncertain Nonlinear System

In this paper, we study the best achievable performance of a nonlinear system with an uncertain parameter vector in an output regulation problem. The nonlinear system is a stabilizable nonminimum phase system and its zero dynamics consists of a robust input-to-state stable component and an unstable but stabilizable component. It is assumed that the uncertain parameter vector, in the form of nonlinear functions, only appears in the robust input-to-state stable component of the zero dynamics and the linearizable part of the system. In the latter, the functions including the uncertain parameter satisfy a lower triangular structure. The performance considered in the output regulation problem for the uncertain nonlinear system is measured by the energy of its output. It is shown in this paper that the best achievable performance of the nonlinear system in the output regulation problem is only determined by the minimum energy of stabilizing the unstable component of its zero dynamics