Minimal-order polynomial satisfying the equality c^Tp(A)=O

Abstract

In the paper, a space P(c,A) of polynomials satisfying the equality cTp(A) = 0 is considered and characterised in detail. As an application, the problem of finding the minimal-order input/output relationship for a discrete-time system x(m + 1) = Ax(m) + Bu(m), y(m) = cTx(m) + d(m) is then related to the problem of identification of the minimal-order polynomial of P(c,A).