Abstract
In a design of control system by polynomial matrix approach, it is important to consider Diophantine equation. Although the methods to solve Diophantine equation are well known, a choice of degree for stable polynomial matrix in Diophantine equation is not discussed sufficiently. In this paper, we consider this problem. As a result, we obtain a Diophantine equation which corresponds to the design of state feedback using minimal order state observer in state space. Using this, we propose a calculation method of doubly coprime factorization which gives more wide class factorization than ordinary methods. We also gives a degree constraint of free parameters in the solution of Diophantine equation which satisfies the properness of controllers.
