Minimization of peak values of signals in feedback systems

In this paper we investigate a dual formulation for the problem of designing linear time-invariant controllers which minimize the maximum value, and/or maximize the minimum value, of signals in the standard one-parameter feedback configuration. The reference input, which is permitted to be unstable, is fixed, and there are no disturbances. Some results concerning the influence of unstable plant poles and zeros, and unstable zeros of the reference input, on achievable overshoot and undershoot reduction are obtained.