Performance Limitation in Output Regulation of an Uncertain Nonlinear System under Disturbances

In this paper, we study the best achievable performance of output regulation for an uncertain nonlinear system under disturbances. 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 and disturbances only enter the robust input-to-state stable component of the zero dynamics and the linearizable part of the system. In the latter, the uncertain functions satisfy lower triangular structure. The performance of this problem is measured by the energy of output signal of above system. It is shown in this paper that the best achievable performance of output regulation under the worst uncertain parameter vector and disturbances for the nonlinear system is only determined by the minimum energy of stabilizing the unstable part of its zero dynamics.