A geometric solution to the squaring down problem

This paper addresses the problem of the squaring down of LTI systems with the tools of the geometric control theory. More precisely, it is shown how a generic system can be turned into a square and invertible system by means of a state-feedback and an output-injection, and of two static units cascaded at the input and at the output of the given system. In this way, key system properties like phase-minimality, relative degree and infinite zero structure are preserved after the squaring down, and the additional invariant zeros introduced can be arbitrarily assigned in the complex plane.