An improved Toeplitz algorithm for polynomial matrix null-space computation

In this paper, we present an improved algorithm to compute the minimal null-space basis of polynomial matrices, a problem which has many applications in control and systems theory. This algorithm takes advantage of the block Toeplitz structure of the Sylvester matrix associated with the polynomial matrix. The analysis of algorithmic complexity and numerical stability shows that the algorithm is reliable and can be considered as an efficient alternative to the well-known pencil (state-space) algorithms found in the literature.