Patchy Solution of a Francis-Byrnes-Isidori Partial Differential Equation

The solution to the nonlinear output regulation problem requires one to solve a first-order partial differential equation, known as the Francis–Byrnes–Isidori equations. In this paper, we propose a method to compute approximate solutions to the Francis–Byrnes–Isidori equations when the zero dynamics of the plant are hyperbolic and the exosystem is two dimensional. With our method, we are able to produce approximations that converge uniformly to the true solution. Our method relies on the periodic nature of two-dimensional analytic center manifolds. Copyright © 2012 John Wiley & Sons, Ltd.