On the synthesis of controllers for continuous time LTI systems that achieve a non-negative impulse response

The problem of controlling the oscillatory response of a system has many practical applications. In this paper, I consider the problem of controlling the sign of the closed loop impulse response for a delay-free LTI system. If the impulse response of a stable system does not change sign, then its step response will neither undershoot nor overshoot. In this paper, I will show that such a synthesis is possible iff the open loop system does not have real, non-minimum phase zeros. In addition, I provide a stable compensator that achieves a stable, non-negative impulse response, if there exists one. (C) 2002 Elsevier Science Ltd. All rights reserved.