Stabilization of a distributed system with a stable compensator

Abstract

It is proved that a multivariable distributed system, that has no poles on the boundary of the half-plane of analyticity of its transfer function, can be stabilized with a stable strictly proper lumped compensator if and only if the standard parity interlacing condition is satisfied. The problem is formulated and solved in a Banach algebra of transfer functions that are Laplace transforms of measures having a finite total variation with respect to some given submultiplicative weight function. In particular, this result can be applied to transfer functions in the Callier-Desoer class, and it seems to be new even for this class. The proofs are closely related to and based on the scalar case solved previously.