A method is proposed for the adaptive control of linear time varying discrete systems. The stability problem of the model reference adaptive control systems is considered by means of the properties of hypergtability, The hyperstability approach also allows for solutions to the adaptation mechanism. Employing the principles of the continuous time case with output feedback renders it to the discrete case which simplified the system design. The system response is obtained by applying the ramp and step input as a reference signal to the system respectively. With checking the adaptation time for ramp and step input the validity of proposed algorithm was confirmed by the computer simulation.