Exact pole assignment by output feedback Part 1

Abstract

ABSTRACT We shall prove that exact assignment of distinct poles using output feedback is possible in any controllable and observable linear time-invariant multivariable system in which the number of inputs plus the number of outputs exceeds the number of states, except in clearly identified circumstances. Furthermore we give a construction for the entire class of pathological cases. The main part of our argument is concerned with the assigning of complex conjugate eigenvalues by means of a real feedback matrix; indeed we begin by giving a simple algorithm which is effective over any field. Although this problem has been discussed by numerous authors in the past, they have usually presented only generic results. We examine the complete class of systems satisfying the hypotheses mentioned.