Design of non-overshooting feedback control systems

The authors consider the problem of designing non-overshooting feedback control systems when the input is a step. They also consider the more general problem of designing controllers to optimally track a step with some predetermined amount of allowable overshoot. It is shown that both these problems always have a solution (under some standard assumptions). It is then shown that the counterpart of this problem, that is, the problem of designing non-undershooting feedback control systems, need not have a solution in general, but it is proved that one can always design a feedback controller to achieve as little percentage of undershoot as desired. Most of the work deals with discrete-time single-input single-output systems though some extensions of the techniques to continuous-systems are discussed