Algebraic and computational aspects of time-delay systems

Abstract

~ = (A, B, C, D).This explains why pole assignability is often a far too strong property to ask for.If the closed-loop system is well posed, the matrix (/+DJ) is invertible over 'R.Defining E := (I+ DJ)-1 , the previous formula can be rewritten as y = ECx-EDHw + EDr.K;(z) adj(K;(z)) = det(K;(z)) I= a:;(z) I.Since K;(z) consistsof n columns of (zi-AIB), it is possible to extend adj(K;(z)) with zero rows on the right places to an (n + m) x n matrix K;(z) in such a way that (zi-AIB) K;(z) = a:;(z) I.