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Abstract.
This paper examines the fundamental limitations on closed-loop
performance imposed by instability in the plant (Right Half Plane
(RHP) poles). 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, and for a one
degree-of-freedom controller the presence of RHP-poles further
deteriorate the response, whereas there is no additional penalty for
having RHP-poles if we use a two degrees-of-freedom controller. 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.