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

Mei Liu, James Lam, Bohao Zhu, Xingjian Jing

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)1406-1417
Number of pages12
JournalInternational Journal of Systems Science
Issue number8
Publication statusPublished - 10 Jun 2020


  • Discrete time
  • negative imaginary systems
  • positive real systems
  • state-space symmetric systems
  • uncertain systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications

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