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On positive realness and negative imaginariness of uncertain discrete-time state-space symmetric systems

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  • Mei Liu
  • James Lam
  • Bohao Zhu
  • Xingjian Jing

Abstract

This paper provides an analysis of uncertain discrete-time negative imaginary and positive real systems with state-space symmetry. First, a necessary and sufficient condition is provided for a minimal state-space symmetric system to be discrete-time positive real or discrete-time negative imaginary. Then, based on the discrete-time symmetric negative imaginary and positive real lemmas, bounds on symmetrically structured perturbations that maintain the negative imaginariness and positive realness of a discrete-time state-space symmetric system are derived. Finally, an RL network example is provided to illustrate the main results of the paper.

Suggested Citation

  • Mei Liu & James Lam & Bohao Zhu & Xingjian Jing, 2020. "On positive realness and negative imaginariness of uncertain discrete-time state-space symmetric systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(8), pages 1406-1417, June.
  • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:8:p:1406-1417
    DOI: 10.1080/00207721.2020.1764129
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