Realization of full column rank precompensators using stabilizing static state feedback

• Suppose a compensator is specified so as to alter the transfer function of the system
• Suppose state feedback is applied to the system to realize the compensation
• Non-square compensators result in non-regular state feedback
• Such a feedback law is not unique and affects the controllability of the system
• Conditions are determined for a stable match to exist

In some control problems, it is convenient to use a precompensator to alter the transfer function of the system such that 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. When the compensator is square and non-singular, the state feedback is regular and the problem has already been solved. Non-square compensators, however, 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.