Performance analysis of output regulation for a class of nonlinear systems

In the paper, Serrani and Isidori design an output feedback controller that achieves semiglobal output regulation for a class of minimum phase nonlinear systems. The controller has three basic components: an internal model to ensure asymptotic regulation, a high-gain partial state feedback controller to stabilize the augmented system of the plant and the internal model, and a high-gain observer to implement the partial state feedback. In this paper we show a property of the transient performance of the controller of. We consider an alternate controller that shares with the controller of the structure of high-gain partial state feedback and high-gain observer, but without internal model. Such controller can only achieve practical regulation. We show that when the controller and observer gains are high enough, the trajectories under the two controllers will be close to each other. This property shows that the transient performance of the controller of is not degraded by the inclusion of the internal model.