COMPUTING NORMAL EXTERNAL DESCRIPTIONS AND FEEDBACK DESIGN

Given a linear system x = Ax + Bu, we compute a normal external descri ption (N(s), D(s)), using the Hessenberg form of the pair (A, B) and e mbedding techniques. We show how to compute a state feedback K that as signs the closed-loop invariant polynomials using a Diophantine equati on. The solution to such an equation corresponds to a back-substitutio n problem, due to the special structure of the computed normal externa l description. A procedure to compute an output matrix C that assigns the desired finite zeros of the system is also outlined in terms of a Diophantine equation. The proposed algorithms are easy to implement an d computationally efficient and therefore can form a useful toolbox in design problems.