Abstract.
This paper examines the limitations imposed by Right Half Plane (RHP) zeros and poles in multivariable feedback systems. The main result is to provide lower bounds on || WXV (s)||infinity where X is the input or output sensitivity or complementary sensitivity. W and V are matrix valued weights who might depend on the plant and who also might be unstable. Previously derived lower bounds on the H-infinity-norm of the sensitivity and the complementary sensitivity are thus generalized to include bounds for reference tracking and disturbance rejection. Furthermore, new bounds which quantify the minimum input usage for stabilization in the presence of measurement noise and disturbances, are derived. From the bounds we find that output performance is only limited if the plant has RHP-zeros. For a one degree-of-freedom (1-DOF) 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 (2-DOF) controller (where the disturbance and/or reference signal is measured). For large classes of plants we prove that the lower bounds given are tight in the sense that there exist stable controllers (possible improper) that achieve the bounds.

Note: This version may be slightly different from the finally published journal paper.