Solution to Morgan´s problem

A necessary and sufficient condition is presented for the solution of the row-by-row decoupling problem (known as Morgan´s problem) in the general case, that is, without any restrictive assumption added to the system to the feedback law u=Fx+Gy (G may be noninvertible). This is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system. These integers are the infinite zero orders (Morse´s list I₄) and the essential orders of the system, which only depend on the input-output behavior, and Morse´s list I₂ of the system, which depends on the choice of a particular state realization