Fast Error-Free Algorithms for Polynomial Matrix Computations

Matrices of polynomials over rings and fields provide a unifying framework for many control system design problems. These include dynamic compensator design, infinite dimensional systems, controllers for nonlinear systems, and even controllers for discrete events stems. An important obstacle for utilizing these powerful mathematical tools in practical applications has been the non-availability of accurate and efficient algorithms to carry through the precise error-free computations required by these algebraic methods. In this paper we develop highly efficient, error-free algorithms, for most of the important computations needed in near systems over fields or rings. We show that the structure of the underlying rings and modules is critical in designing such algorithms.