The models that can be matched by feedback

Abstract

Model matching (or exact model matching) is a problem of great interest in systems theory and applications. It consists of compensating a given system so as to achieve a specified target transfer function matrix. For linear time-invariant systems and regular static state feedback compensation, the solution is well known. The non-regular case, when the number of external inputs does not match the number of control inputs, the problem has not been solved until recently. The solution is not entirely algorithmic and requires some kind of trial and error. That is why it may be of interest to be able to decide on solvability prior to determining a solution. This is made possible by an efficient parametrization of all target models that can be matched by feedback applied to the given system.