The Infinite-dimensional Sylvester Differential Equation and Periodic Output Regulation

In this paper the solvability of the infinite-dimensional Sylvester differential equation is considered.Th is is an operator differential equation on a Banach space.Con ditions for the existence of a unique classical solution to the equation are presented.In addition, a periodic version of the equation is studied and conditions for the existence of a unique periodic solution are given.Th ese results are applied to generalize a theorem which characterizes the controllers achieving output regulation of a distributed parameter system with a nonautonomous signal generator.