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In Karampetakis (1995) an algorithm for computing the generalized inverse of a singular polynomial matrix A(s) ∈ R[s] n×m has been presented. In this paper the algorithm is extended to that of the singular rational matrix, A(s) ∈ R(s) n×m , and the algorithm is subsequently implemented in the symbolic computational package Maple. Several applications of its use are given.

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On matrix pencil equivalents of a general polynomial matrix," Int. J. Contr., vol. 49, S.-Y. Zhang, "Generalized proper inverse of polynomial matrices and the existence of infinite decoupling zeros," IEEE Trans. Au-tomat.The infinite elementary divisors of a matrix polynomial and implications," Int. J.A unification of system transformations," in Proc. ACC-88, Atlanta, GA, 1988, vol. A. C. Pugh and G. E. Hayton, Realization and Modeling in System Theory, M. A. Kaashoek, J. H. van Schuppen, and A. C. M. Ran, Eds. Cambridge, M A Birkhauser, pp. 107-116, 1990. "Transfor-mation issues in linear system theory," also in Proc. MTNS-89, to be published. A. C. Pugh and P. A. Ratcliffe, "On the zeros and poles of a rational matrix," Int. Abstract-In this note, we present an alternative stability analysis for recent results on global stabilization of a nonlinear system in cascade with a linear system. The analysis is carried out using passivity arguments. We also present the relationship between passivity and an important class of Lyapunov functions.