Achievable input performance of linear systems under feedback control.

Abstract

In this paper, we characterize the achievable input performance

for linear time invariant systems under feedback control. We provide analytical expressions for minimal input requirement for

stabilization in both of the H2 and H-inf optimal control frameworks. The achievable input performance primarily depends on

the joint controllability and observability of unstable poles. These results are also extended to systems with time delay. It is

shown that time delay poses no serious limitations on the achievable input performance for systems with slow instabilities and vice versa. The proposed results unify the available results on input performance limitations and are useful for

various purposes including selection of variables for the stabilizing layer, process design and formulation of the optimal

controller design problem.