Effects of radial shifts of eigenvalues on norms of linear systems

Abstract

We show that for linear systems represented in the controllable canonical form there are simple and systematic changes in the input/output properties of the closed-loop system from the disturbance input to the system output when controls are applied to produce a radial displacement of all the closed-loop poles. In particular this is true for the transfer function and the impulse response of the systems. This in turn leads to a better understanding of how such changes in the control gains affect the induced L/sub 2/ norm, (the H/sub 2/ norm) and the induced L/sub /spl infin// norm (the L/sub 1/ norm) of the system.