Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems

Sei Zhen Khong, Ian R. Petersen, Anders Rantzer

Research output: Contribution to journalArticlepeer-review

Abstract

Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are shown to be sufficient and necessary for closed-loop stability along a homotopy of systems.

Original languageEnglish
Pages (from-to)310-316
Number of pages7
JournalAutomatica
Volume90
DOIs
Publication statusPublished - 2018 Apr 1

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • Distributed-parameter systems
  • Integral quadratic constraints
  • Negative imaginary systems
  • Robust feedback stability

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