Robust practical output regulation of rational nonlinear systems via numerical approximations to the regulator equations

This article presents a systematic framework able to synthesize error- and state-feedback internal model controllers for the robust practical output regulation of rational nonlinear plants subject to linear exosystems. In order to approximate the system zero-error steady-state condition, we consider the use of polynomial mappings with respect to a set of relaxed regulator equations. This methodology allows the implementation of simplified internal models, which is useful to reduce the controller order and also to deal with cases where an exact internal model immersion is unknown. By using a differential-algebraic representation, our method can be systematically applied to any plant with rational dynamics, including those that cannot be expressed by triangular forms, such as illustrated in the examples. The closed-loop stabilization problem is carried out in the form of convex optimization problems subject to linear matrix inequality conditions, allowing us to provide rigorous guarantees such as the ultimate boundedness of the output error norm and the exponential convergence of the system trajectories within a minimum decay-rate.