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 H 2 and H 1 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

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... 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.