An explicit expression for the minimum-phase image of transfer function matrices

A simple expression is obtained for the transfer function matrix of the minimum-phase image of a left invertible continuous-time invariant system with zeros in the right half-plane that may be of multiplicities greater than one. This expression is obtained by multiplying the system transfer function matrix, from the right, by a special inner matrix, and it is explicitly given in terms of the input zero directions that correspond to the zeros of the system in the right half-plane. The result provides a simple expression for the inner-outer factorization of transfer function matrices, and it can thus be used in H_∞-optimal control