Realization of precompensators via stabilizing non-regular static state feedback

In some control problems, it is convenient to use a precompensator to alter the transfer function of the system so as the transfer function of the compensated system has a specified property. Then, if possible, the action of the compensator on the system is realized by a static state feedback law applied to the system. Non-square compensators result in non-regular state feedback. In this paper, necessary and sufficient conditions are presented for the compensated system to be stabilizable by such a non-regular static state feedback law.