The problem of asymptotic regulation of the output of a dynamical system plays a central role in control theory. An important variant of this problem is the output regulation problem, which can be used in areas such as s- point control, tracking reference signals and rejecting disturbances generated by an external system, controlled synchronization of dynamical systems, and observer design for autonomous systems. At the moment this is a hot topic in nonlinear control. This book is a result of a four-year research project conducted at the Eindhoven University of Technology. This project, entitled “Robust output regulation for complex dynamical systems,” began with the observation that theproblemofcontrolledsynchronizationofdynamicalsystemscanbecons- ered as a particular case of the output regulation problem. In the beginning of the project, known solutions to the controlled synchronization problem were global and dealt with nonlinear systems having complex (“chaotic”) dyn- ics. At the same time, most of the existing solutions to the nonlinear output regulation problem were local and dealt mostly with exosystems being linear harmonicoscillators. Ourinitialideawas,usingtheresultsfromthecontrolled synchronization problem as a starting point, to extend solutions of the n- linear output regulation problem from the local case to the global case and to avoid restrictive assumptions on the exosystem. As a ?rst step, we started looking for points that were common to these two problems.