Overshoot analysis for a family of linear systems subject to bounded reference inputs

It is usually difficult to analyze the response overshoot of a high order linear system, because the corresponding inverse Laplace transform of the response is difficult to compute analytically. In this paper, we use a novel method to analyze the response overshoot of a family of stable linear systems whose orders may be arbitrarily high. This method is characterized by the construction of equivalent realization of the systems and the idea of proof by contradiction. The result is that the responses of these systems for any bounded reference inputs must overshoot. This result covers some existing results in literature. Several guidelines for non-overshooting controller design are also obtained. And three examples are given to confirm the theory result.