Abstract: An equivalence theorem was derived to determine if the transfer matrixH∞-norm between two linear systems [A,B,C,D] and [A+BR-1DTC,BR-1/2,(I+DR-1DT)1/2C,0] is smaller than 1. This theoremwas then used to derive another theorem about the stability of system [A,B,C,D]. This equivalence theorem simplifies the proof of the theorem about the stability of system [A,B,C,D] and determination ofH∞-norm. An algorithm for computing theH∞-norm of the transfer matrix of system[A, B,C,D] was presented.