Homotopic invariance of the decentralized eigenvalue placement property

The purpose of this paper is to determine conditions on a linear time independent interconnected systems such that the spectrum of the system can be arbitrarly assigned by decentralized output feedback. It is shown that with appropriate dynamic compensation class of systems A = {A} for which the conditions hold is a generic subset in the set of all systems of the same dimensions. Further it will be shown that on {A} the decentralized eigenvalue placement property is a homotopic invariant. Hence the feedback needed to realize a particular spectrum can be computed by a homotopic continuation method.