A geometric paradigm exposing high gain root sensitivity of single-input single-output systems

Abstract: "Relationships useful for analysis and design exist between the magnitude of the classical root sensitivity function at high gainand the asymptotic behavior of eigenvalue magnitudes. These relationships are proven rigorously via mathematical analyses of closed loop single-input single-output systems whose eigenvalue magnitudes are predictable at high gain. More powerfully, the relationships are demonstrated via geometric arguments employing magnitude gain plots depicting eigenvalue magnitude as an explicit function of gain. Two theorems summarize the major results of high gain sensitivity magnitude behavior; a third theorem applicable for all gains relates root sensitivities toslopes of the magnitude gain plot."