The regulator equations for retarded delay differential equations

In this work we present a simple formula for the solution of problems of output regulation (tracking and disturbance rejection) for systems governed by linear retarded functional differential equations. Our formulas are based on an analysis of the so-called regulator equations. In the geometric theory of output regulation the desired feedback gain is obtained from solution of these equations. For delay equations we show that the regulator equations reduce to a pair of finite dimensional linear systems of equations. For special exosystems we give an explicit formula for the solution.