Exact computation of frequency responses for a class of infinite dimensional systems

We develop a method for the exact computation of the frequency responses for a class of infinite dimensional systems. In particular, we consider the distributed parameter systems in which a spatial independent variable belongs to a finite interval. We show that an explicit formula for the frequency responses can be derived whenever the underlying operators can be represented by a forced two point boundary value state-space realizations (TPBVSR). This formula involves finite dimensional computations with matrices whose dimension is at most four times larger than the order of the underlying differential operator. In this way an exact reduction of an infinite dimensional problem to a finite dimensional one is accomplished. We also provide several examples to illustrate the procedure.