Computing Normal External Descriptions and Feedback Design

Given a linear system ¿= Ax + Bu, we compute a normal external description (N(s), D(s)), using the Hessenberg form of the pair (A, B) and embedding techniques. We show how to compute a state feedback K that assigns the closed-loop invariant polynomials using a Diophantine equation. The solution to such an equation corresponds to a back substitution problem due to the special structure of the computed normal external description. The proposed algorithms are easy to implement and computationally efficient.