Zero Assignment and Model Matching by Using Two-delay Input Control

Abstract

Model matching is one of the direct methods by which the characteristics of a controlled system can be adjusted to the desired values. It is well known that poles can be assigned by state feedback, but zeros are invariant under state feedback. So, we have difficulty in constructing a model matching system if the system has unstable zeros.
By using two-delay input control and state feedback, Mita et al. has shown that invariant zeros can be assigned and a model matching can be realized.
In this paper, we give a different proof to the necessary and sufficient condition that the invariant zeros can be arbitrarily assigned. Through this proof, it is made clear which element of the feedback gain relates to zero assignments. It is also shown that invariant zeros and poles can be arbitrarily assigned if and only if the two-delay input control system has no zeros. By the proof using coordinate transformation, the straightforward algorithm is obtained for the determination of feedback gains for model matching.
Zeros are assignable under the same condition, if the state feedback is replaced by an observer and its feedback.