Output regulation for linear distributed parameter systems

This work extends the geometric theory of output regulation to linear distr ibuted parameter systems with bounded input and output operator, in the cas e when the reference signal and disturbances are generated by a finite dime nsional exogenous system. In particular, it is shown that the full state fe edback and error feedback regulator problems are solvable, under the standa rd assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter system s this represents an extension of the geometric theory of output regulation developed in [10] and [4], We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and t he system transfer function. Examples are given of periodic tracking, set p oint control, and disturbance attenuation for parabolic systems and periodi c tracking for a damped hyperbolic system.