Polynomial Equations: A Tool for Control Systems Synthesis

Abstract

Motivated by the pole placement design techniques, linear polynomial (or diophantine) equations have become a popular design tool of control engineers. The paper presents the theory, properties, and computational algorithms for the equation ax + by = c in a tutorial manner. Recent results are presented on the parametrization of limited degreee solutions, of relatively prime solutions, and of solutions x, y such that y/x is proper rational. Parametric and non-parametric computational algorithms are discussed in detail.