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 PDE, known as the Francis-Byrnes-Isidori (FBI) equations. In this paper we propose a method to compute approximate solutions to the FBI 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. 
Cesar O. Aguilar and Arthur J. Krener
math.OC cs.SY math.DS