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Abstract.
This paper examines the fundamental limitations imposed by instability
in the plant (Right Half Plane (RHP) poles) on closed-loop
performance. The main limitation is that instability requires active
use of plant inputs, and we quantify this is terms of tight lower
bounds on the input magnitudes required for disturbance and
measurement noise rejection. These new bounds involve the
H-infinity-norm, which has direct engineering significance. The output
performance in terms of disturbance rejection or reference tracking is
only limited if the plant has RHP-zeros. It is important to stress
that the derived bounds are controller independent and that they are
tight, meaning that there exists controllers which achieve the lower
bounds.