Asymptotic behavior of multivariable and optimal system designs

Abstract: "In this report we investigate the high gain asymptotic behavior of multivariable root loci. The proposed method groups the unbounded root loci of a non-singular m-input/m-output system into several Butterworth patterns as the gain tends toward infinity. A geometric technique provides direct realization of these asymptotic Butterworth patterns. Since integer as well as non-integer orders of these patterns can be determined, the method can be used to identify undesirable design conditions. Finally, the proposed method is extended to linear quadratic regulator problems where optimal root loci are identified. Three examples are presented to illustrate the effectiveness of the approach."