Abstract: "This paper quantifies and summarizes in a general theorem the asymptotic high gain behavior of closed-loop eigenvalues. The theorem is founded on fundamental principles of classical control theory, and its implications are demonstrated conclusively via specialized plots, the Gain Plots (Kurfess and Nagurka, 1991), that offer a new and revealing graphical perspective. The theorem defines the rate (with respect to change in gain) at which closed-loop eigenvalues migrate towards both finite and infinite transmission zeros. This sensitivity information is essential for complete design of control systems in terms of gain selection and its relationship to stability, performance, and robustness. The general theory is graphically related to the classical control definition of sensitivity."