Synthesis of robust tracking systems with specified transfer matrices

In this paper we study linear time-invariant multivariable systems in which the compensators consist of both feedforward and feedback parts. Firstly, a necessary and sufficient condition for the system to be an internally stable robust tracking system is obtained. Secondly, the class of attainable transfer matrices from reference signal to plant output of internally stable robust tracking systems is clarified. Thirdly, a simple method is proposed for specifying two feedback properties, i.e., sensitivity and stability margin. Finally, based on these results, we propose a synthesis procedure of robust tracking systems with desirable transient responses, sensitivity and stability margin