Simultaneous Transformation of Systems to a Form with Relative Degree

We consider the problem of transforming two linear control systems to a form with relative degree by one and the same linear time-invariant change of outputs. A constructive algorithm is proposed that permits one to verify if this problem has a solution, and if it does, find the desired change. Moreover, it is shown that transforming three control systems by one and the same linear time-invariant change of outputs to a form with relative degree is not always possible.