An algebraic approach to solve the model matching problem for single input single output systems

In this communique, an algorithm is proposed to solve symbolically the model matching problem for single input single output systems. A solution to such a problem has been proposed in Doyle et al. (1990) using the Nevanlinna–Pick theory. However, when implementing such a procedure numerically, some issues may arise due to imperfect cancellations among the numerator and the denominator of the obtained controller. The proposed algorithm overcomes such issues by using some algebraic geometry results to solve exactly the problem.