Robustness of d-stability for discrete large-scale uncertain systems

Chien Hua Lee, Tzuu Hseng S. Li, Fan Chu Kung

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Based on Lyapunov stability theory associated with transformation techniques, the D-stability robustness problem is first discussed for discrete large-scale systems subjected to interconnections and perturbations. Three classes of perturbation are treated: (1) unstructured parametric perturbations; (2) highly structured parametric perturbations; and (3) nonlinear perturbations. If all the eigenvalues of each nominal subsystem are located inside the specified discs Di(∝i, ri), respectively, sufficient conditions for D-stability are presented to guarantee that all the eigenvalues of each perturbed subsystem remain inside the same discs. Furthermore, the proposed D-stability criteria ensure that the whole discrete large-scale system is D-stable irrespective of perturbations and interconnections if the eigenvalues of each nominal subsystem lie within the same disk D(∝, r). By these conditions, the allowable perturbation bounds that ensure the D-stability of discrete large-scale perturbed system can be estimated. Finally, numerical examples are given for illustration.

Original languageEnglish
Pages (from-to)479-498
Number of pages20
JournalInternational Journal of Systems Science
Volume24
Issue number3
DOIs
Publication statusPublished - 1993 Mar

All Science Journal Classification (ASJC) codes

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

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