Polynomial solutions to regulation equations with nonlinear exosystems

Solving a regulation equation is the core part of output regulation problem. It remains as a challenge to find a solution for a general case of output regulation with nonlinear exosystems. This paper identifies certain conditions for the existence of a polynomial solution, and propose an iterative method for obtaining polynomial solutions for regulation equations with nonlinear exosystems. The proposed solution is then applied for the internal model design in output regulation of nonlinear systems.