" _ Xi!NxN -F^t) -INxN Vnxn 0 _1 * J ) - -H* 0 . _*NxN 0 0 (6-15) The right-hand side of (6-15) is a 3Nx3N matrix which is readily seen to have full rank for all Aj. The fact that this matrix is full rank for any A^ means that the stability condition can be achieved regardless of the eigenvalues of the internal model system. In otherwords, the frequencies of the reference and disturbance signals will not be a factor in deciding whether or not the stability condition can be met. By showing that both conditions (1) and (2) hold, we have proven that it is possible to stabilize the linearized manipulator system (assuming the slowly time-varying approach will apply).