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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 thedoi:10.1080/00207170500204815 fatcat:e77u5djdlzhcfpmmq6lo4ej3oi