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Stability analysis of sampled-data systems via open-/closed-loop characteristic polynomials contraposition

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  • J. Zhou
  • H. M. Qian

Abstract

In this paper, a class of sampled-data systems with double feedbacks are scrutinized for internal/external stability through the open-/closed-loop characteristic polynomials contraposition. A sampled-data system with double feedbacks consists of a continuous-time plant and two feedback control loops: a discrete-time one for digital control objectives with sampler and zero-order hold synchronized, and a continuous-time one for analog control performances. Contraposition stability criteria are worked out by exploiting what we call the contraposition return difference relationship in between the open- and closed-loop characteristic polynomials defined via the lifted model. The criteria for asymptotical stability are necessary and sufficient, independent of open-loop poles distribution of the lifted model and locus orientation specification. Moreover, the criteria for Lp-stability are sufficient, while retaining the technical merits of the criteria for asymptotical stability. All criteria present stability conditions in the standard discrete-time sense that are implementable either graphically with loci plotting, or numerically without loci plotting. Examples are included to illustrate the results.

Suggested Citation

  • J. Zhou & H. M. Qian, 2017. "Stability analysis of sampled-data systems via open-/closed-loop characteristic polynomials contraposition," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(9), pages 1941-1953, July.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:9:p:1941-1953
    DOI: 10.1080/00207721.2017.1290298
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