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Fundamental limitations for control of unstable SISO plants. K. Havre and S. Skogestad, Submitted for publication in Automatica, October 1997.

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.