Controller synthesis for sign-invariant impulse response Academic Article uri icon


  • In this note, we consider the problem of designing controllers for discrete-time linear time-invariant (LTI) plants that render the closed-loop impulse response nonnegative. Such systems have a nonundershooting and nonovershooting 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, nonminimum phase plant zeros. Finally, we show, by construction, how such a compensator may be synthesized when the plant does satisfy the existence condition.

published proceedings


author list (cited authors)

  • Darbha, S., & Bhattacharyya, S. P.

citation count

  • 20

complete list of authors

  • Darbha, S||Bhattacharyya, SP

publication date

  • August 2002