A method for the expansion of matrix-fraction description (Q1823905)

Let the transfer matrix of a finite-dimensional linear system be given as a left coprime factorization \(H(s)=D^{-1}(s)N(s)\) where the polynomial matrices D(s) and N(s) are given. A fraction description of H(s) is given as a finite sum of terms \(L_{i,j}(s-\lambda_ i)^ j\), where the \(\lambda_ i's\) are the roots (counted with their multiplicity) of det D(s). The paper provides a simple explicit method for computing the matrices \(L_{i,j}\) in such a matrix fraction expansion.