 
Summary: 978 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 34, NO. 9, SEPTEMBER 1989
Technical Notes and Correspondence
On Stable Solutions of the One and Twosided Model
Matching Problems
ZHIQIANG GAO AND PANOS J. ANTSAKLIS
AbstractAn algorithm is introduced to determine proper and stable
solutions to the model matching problem. It utilizes the theory of inverses
and statespace algorithms, and it guarantees a proper and stable solution
to the problem when one exists. This approach is also used to determine
proper and stable solutions of the twosided matching problem. Examples
are included.
I. INTRODUCTION
The model matching problem (MMP) is defined as follows. Given
proper rational matrices P(p x m ) and T(p X q),find a proper rational
matrix M such that the equation
PM= T (1)
holds. This problem is also being referred to as the exact model matching
problem.
The model matching problem has drawn the attention of many
researchers both because of its importance in control and its attractive
