Decoupling of square linear systems with delays

The aim of this paper is to exhibit matricial necessary and sufficient conditions for the decoupling problem of linear systems with commensurate delays, under static nonpredictive and stable state feedbacks. A “matrix” approach is used which is similar to the Falb-Wolovich one for systems without delay. The conditions obtained here are quite simple, easily computable, and less restrictive than the previous ones. Moreover, we give the only possible design of the physically realizable control law that satisfies the problem