This paper shows some relation between the matrices (Hurwitz H, Routh R and Liapunov S:=x^TSx) for stability criterion and the performance index in the optimum control for linear constant coefficient systems. In the process of this research, some new meanings of H and S, in the view point of optimum control, are investigated.
As a result, it is shown that the relation between H, R and S can be described more compactly than conventional ways. Furthermore, this paper shows the direction of its application, through some examples.