Necessary and Sufficient Condition for Stability of Switched Uncertain Linear Systems under Dwell-Time Constraint

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66 Scopus citations

Abstract

In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing a class of time-scheduled homogeneous polynomial Lyapunov functions with a sufficiently large degree. The key feature of this nonconservative condition lies in its convexity in the system matrices, which explicitly facilitates its further extension to uncertain systems. Then, in order to obtain numerically testable condition, a family of LMI conditions are presented with the aid of the idea of dividing the dwell-time interval into a finite number of segments. It is proved that the non-conservativeness can be maintained with a sufficiently large interval dividing parameter. In the end, the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices. Numerical examples are presented to illustrate our findings.

Original languageEnglish (US)
Article number7397943
Pages (from-to)3619-3624
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume61
Issue number11
DOIs
StatePublished - Nov 2016
Externally publishedYes

Keywords

  • Dwell time
  • Lyapunov function
  • homogeneous polynomial
  • stability
  • switched system
  • uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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