Simultaneous Squaring Down and Zeros Cancellation in Linear Systems

The problem of simultaneously squaring down and cancelling a specified part of the zeros of a completely general linear system by an invertible transformation is investigated from different standpoints. Various classes of solutions featuring minimal McMillan degree, unitary or J-inner symmetry, either with respect to the imaginary axis or the unit circle are characterized in a realisation-based setting. Several applications in control systems including the problems of squaring down with dynamical zeros allocation or the sub optimal H
^∞
control are indicated.