The use of zeros and zero-directions in model reduction

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 map C. 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.