On the synthesis of multivariable systems

The general question of compensating a linear multivariable system via linear state variable feedback (lsvf) in combination with input dynamics is considered. In particular, it is shown that, since lsvf and input dynamics can both be represented by proper feedforward compensation, any design based on feedforward compensation alone can usually be realized in a more efficient manner through the combined use of "low-order" feedforward compensation (input dynamics) and lsvf. A major result of this paper is the frequency-domain synthesis algorithm outlined in Section III for "separating" any proper feedforward transfer matrix in order to achieve the more efficient compensation scheme. Specific examples which illustrate the employment of the algorithm to the questions of decoupling and exact model matching are also included.