Matrix fraction descriptions of linear time-invariant systems

In this paper an algorithm is presented for obtaining a relatively prime matrix fraction description (MFD) for a time-invariant linear system in state space form not necessarily of minimal dimension. The algorithm first performs a sequence of simple coordinate transformations on the state vector of the system. The observability (controllability) indices of the system are also determined at this time. The relatively prime factors of an MFD are then obtained via a recursive procedure involving the submatrices of the state and the input matrix of the transformed state space system. A numerical example is given to illustrate the use of the algorithm.