OPTIMAL ROOT LOCI OF LINEAR-MULTIVARIABLE SYSTEMS

One aspect of the behavior of optimal systems which has received little attention concerns the movement of the closed-loop poles of optimal systems when the weight on the control efforts in the index of performance is relaxed to arbitrarily low levels. Results have been derived for scalar systems only while extensions of these to the multivariable case have been presented in a qualitative manner only with the exception of the lowest order of behavior for which some explicit results exist. Here a new root-locus approach is used in order to study all orders of behavior. The results derived relate the asymptotic behavior of the poles of the optimal system to that of the original system and for this reason more light is cast onto the function of the optimal controller