We establish structural controllability results for matrix pairs [A, B] where .4=A0+Z piAi, B=B,+Z piB', with tho At, Bi fixed, and the pr free scalar parameters. Tho results characterize structural controllability in several wsys, via, tests involving the cllecking of the rank or the evaluation of the determinant of various constant matrices formed from t,he At, Bi. A number of the result,^ us...