A simple division method for solving Diophantine equations and associated problems

Abstract

Based on the transfer function matrices or the matrix fraction descriptions of multivariable systems, a simple division method in conjunction with the method owing to Wolovich and Antsaklis (1984) is presented in this paper for obtaining the observability and controllability indices, the irreducible right (left) matrix fraction descriptions from reducible or irreducible left (right) matrix fraction descriptions, the greatest common divisors of two polynomial matrices and the solution of a Diophantine equation, without utilizing the state-space realization of the matrix Traction description.