Performance limitations for unstable SISO plants

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_∞-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