Reduction of linear systems to a form with relative degree using minimum-phase output transformation

Abstract

A normal form is one of the canonical forms frequently used in control theory for linear time-invariant systems. Only systems with a relative degree can be reduced to such a form. Although a control system does not necessarily have a relative degree, in a sufficiently general case there exists a stable dynamic output transformation reducing the system to a system with a relative degree. We prove that this dynamic transformation can be chosen in such a way that the inverse transformation is stable as well.