A new look at transfer function design

This is a review paper. It is written for engineers, in particular practicing control engineers, who are familiar with transfer functions but not with state-variable techniques. The objective of this paper is threefold. First, it is intended to supplement a recent invited paper. (See A. E. Bryson, Jr., and D. G. Luenberger in Proc. IEEE, vol. 58, Nov. 1970, pp. 1803-1811.) The results introduced there by use of state-variable concepts are redeveloped in the frequency domain. Second, it demonstrates to engineers that, for the class of single-input multiple-output systems and multiple-input single-output systems, some of the results developed in state-variable equations can be obtained directly in transfer functions, even with less computation. Finally, the advantage and the limitation of the transfer function approach are discussed.