Design of linear quadratic regulators : the low error weighting case

Abstract: "The branches of optimal root loci that approach infinity as the error weighting is decreased can be characterized by a combination of several Butterworth patterns existing on separate Riemann sheets. Algorithmic approaches have been reported to find the order of these Butterworth patterns. This report presents a geometric technique, involving eigenvalue polar plots, that provides direct realization of the directions and radii of the asymptotic eigenvalue patterns. A graphically- based systematic procedure is proposed and employed in a sample problem for analyzing Butterworth patterns."