Abstract
This paper presents a new algorithm to solve the polynomial Diophantine equation (DE); A(s)X(s)+B(s)Y(s)=C(s), which plays the key role in the design of the feedback control systems. The proposed algorithm (PA), which is based on the backward substitution, consists of the simple algorithm. Comparing the previous ones, it is shown through the theoretical considerations that PA has two advantages. The first is the high freedom of the degree associated with a given polynomial and the solution. The second is that the amount of the operation number, in the sense of arithmetic operation, of PA is remarkable reduced. Furthermore, it is shown that the applying PA to the polynomial matrix DE is easy under suitable conditions.
