The exact bound for robust stability of linear state space with structured uncertainty

Sheng-Fuu Lin*, An Ping Wang

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The exact bound of the unknown parameter for robust stability of linear system in state-space form is presented in this paper. If all unknown parameters are inside this bound, the real part of all eigenvalues are negative and the system is stable. If there are some parameters outsidc the bound, there is at least one eigenvalue with positive real part and the system is unstable. Hence, the exact bound obtained here is sufficiently necessary condition for the robust stability of a linear state space system. The bound is represented as a set of multi-linear equations of unknown parameters. A direct calculation procedure to obtain the bound is also given.

Original languageEnglish
Pages (from-to)141-146
Number of pages6
JournalJournal of the Chinese Institute of Electrical Engineering, Transactions of the Chinese Institute of Engineers, Series E/Chung KuoTien Chi Kung Chieng Hsueh K'an
Volume9
Issue number2
StatePublished - 1 May 2002

Keywords

  • Linear state space system
  • Multi-linear function
  • Robust stability
  • Routh-Hurwitz criterion

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