Abstract
This paper conciders an inhomogeneous bilinear realization in case of unknown initial state. This problem was first studied by Tarn and Nonoyama. However, their existence condition of inhomogeneous realization is found to be insufficient. Hence, a complete condition is given in this paper.
And their condition of inhomogeneous bilinear realization depends on the factorization of the generalized Hankel matrix into specific factors. This is difficult to check. In this paper, the criteria for judging whether a given matrix has the specific factorization or not are obtained. As a result an existence condition of inhomogeneous bilinear realization is given. The condition is independent of the specific factorization, hence is easy to use for practical purposes.
