Representation of Feedback Operators for Hyperbolic Partial Differential Equation Control Problems

In this paper we present results on existence and regularity of integral representations of feedback operators arising from hyperbolic PDE control problems. The existence of such representations is important for the design of low order compensators and for the placement of sensors. This paper contains results which apply to problems with spatial domains in N dimensions. Numerical examples are included in which the theory is applied to Euler-Bernoulli beams for cases of Kelvin-Voigt and structural damping.