The concept of zeros and zero-directions of a linear time-invariant multivariable system is applied to the problem of shifting eigenvectors into the kernel of the information extraction mapC. By making the maximum number of the closed system modes unobservable, a lower-order transfer-function matrix is obtained. The state feedback structure reducing the model to one of lower dimensions does not exploit all of the degrees of freedom. A part of them are used for pole allocation of the remaining observable poles using a dyadic feedback technique. The suggested technique is applied to reduce a broad class of multivariable systems into first-order multivariable systems. Finally, a dynamical structure realizing the same objectives is introduced.