Performance Limitation in Output Regulation of a Nonlinear System under Disturbance

In this paper, we study the best achievable performance of a nonlinear system under disturbance in an output regulation problem. The nonlinear system is a stabilizable nonminimum phase system and its zero dynamics consists of an input-to-state stable component and an unstable but stabilizable component. It is assumed that a disturbance signal appears in the input-to-state stable component of the zero dynamics and the linearizable part of the system under a lower triangular structure. The performance considered in the output regulation problem for this 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