Algorithms for the Solution of Polynomial Equations Arising in Multivarible Control Theory

In this paper, algorithms are developed for the solution of several problems arising in linear multivariable control theory. The algorithms are based on a modification of a recent algorithm by Kung and Kailath⁴ for the construction of a minimal basis for the left kernel of a polynomial matrix. The basis constructed here is called a modified minimal basis (MMB) and is shown to be of significance in the solutions of the polynomial equations X(s)N(s) + Y(s)D(s) = C(s) and X(s)N(s) + D(s)Y(s) = C(s).