Root-loci concepts for kth-order-type multivariable structures

With the philosophy that many physical multivariable systems can, for the purposes of control-system design be approximately represented by much simpler models, and that the theoretical analysis of such models can provide valuable insight into the time- and frequency-domain characteristics of the system, the paper extends previous work by providing an analysis of a class of multivariable structures analogous to the classical kth-order lag. It is shown that the system can be decoupled by state feedback using parameters defined by the inverse-transferfunction matrix. In more general situations, it is shown that an analysis of the asymptotic form of the system root locus provides valuable insight into the desirable controller structures, and the analysis of the sensitivity of the root locus to controller parameters provides analytic solutions to the feedback-control problem in the cases k = 1, k = 2.