Controller Synthesis for Sign Invariant Impulse Response
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In this paper, we consider the problem of designing controllers for discrete-time LTI plants that render the closed loop impulse response non-negative. Such systems have a non-undershooting and non-overshooting step response. We first show that the impulse response of any discrete-time LTI system changes sign at least "r" times if it has "r" real, positive zeros outside a circular disk centered at the origin and containing all its poles. We then show that a necessary and sufficient condition on the plant for the existence of a compensator that makes the closed loop impulse response sign invariant is that there be no real, positive, non-minimum phase plant zeros. Finally, we show, by construction, how such a compensator may be synthesized when the plant does satisfy the existence condition.
author list (cited authors)
Darbha, S., & Bhattacharyya, S. P.