Study of Inverse Systems Using Matrix Methods

Efficient computation of generalized inverses of rational matrices using orthogonal reduction

Abstract

We address the numerically reliablecomputation of generalized inverses of ra­tional matrices in descriptorstate-space representation. We put particular em­phasis on two classes ofinverses: the weak generalized inverse and the Moore- Penrose pseudoinverse. Bycombining the underlying computational techniques, other types of inverses ofrational matrices can be computed as well. The main computational ingredient todetermine generalized inverses is the orthogonal reduction of the system matrixpencil to appropriate Kronecker-like forms.