This note derives persistence of conditions on the input for systems with partially known transfer functions. The assumed transfer function model is [po(s) + (KP)-P-T(s)]/[q(0)(s) + K(T)Q(s)], where K is the unknown parameter vector p(0)(s), q(0)(s) are known scalar polynomials and P(s) and Q(s) are known vector polynomials.