On computing J-inner-outer factorizations of rational matrices

Proposes a new numerically reliable computational approach to determine the J-inner-outer factorization of a rational matrix G. The proposed approach is completely general being applicable whenever G is proper or not, or of full column/row rank or not. In contrast to existing "one-shot" methods which require the solution of Riccati or generalized Riccati equations, the new approach is recursive and avoids such computationally involved steps by using instead a recursive state-space approach. The resulting factors have always minimal order descriptor representations.