Squaring down with zeros cancellation in generalized systems

Squaring down with simultaneous zeros cancellation by series compensation of a general (possibly polynomial or improper) linear system is investigated. All static and dynamical compensators that spotlight minimal McMillan degree are parameterized. This general result is particularized to get compensators that preserve the L2L2 or L∞L∞ norm of the original system, either in continuous or discrete-time. All results are completely general, numerically sound, and based on general realizations allowing for poles at infinity.