Geometric analysis of multivariable control systems

Abstract: "This report promotes a new graphical representation of the behavior of linear, time-invariant, multivariable systems highly suited for exploring the influence of closed-loop system parameters. The development is based on the adjustment of a scalar control gain cascaded with a square multivariable plant embedded in an output feedback configuration. By tracking the closed-loop eigenvalues as an explicit function of gain, it is possible to visualize the multivariable root loci in a set of 'gain plots' consisting of two graphs: (i) magnitude ofsystem eigenvalues vs. gain, and (ii) argument (angle) of system eigenvalues vs. gain.By depicting unambiguously the polar coordinates of each eigenvalue in the complex plane, the gain plots complement the standard multi-input, multi-output root locus plot. Two example problems demonstrate the utility of gain plots for interpreting linear multivariable system behavior."