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Performance limitations for unstable SISO plants. K. Havre and S. Skogestad, Draft paper submitted to 1998 American Control Conference, Philadelphia, June 1998.

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 the active use of plant inputs, and we quantify this is terms of tight lower bounds on the input magnitudes required when there are disturbances or measurement noise. 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 also 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.