Stability and £ 2 gain analysis for discrete - Time LTI systems with controller failures

Research output: Contribution to journalConference article

Abstract

In this paper, we analyze stability and £ 2 gain properties for discrete-time linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system's stability and £ 2 gain properties are preserved to a desired level. For stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For £ 2 gain, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted £ 2 gain level, and the weighted £2 gain approaches normal £ 2 gain when the ATBCF is sufficiently large.

Original languageEnglish
Pages (from-to)545-550
Number of pages6
JournalIFAC Proceedings Volumes (IFAC-PapersOnline)
Volume37
Issue number11
DOIs
Publication statusPublished - 2004 Jan 1
Event10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, LSS 2004 - Osaka, Japan
Duration: 2004 Jul 262004 Jul 28

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Controllers
Lyapunov functions
Asymptotic stability
System stability
Feedback

Keywords

  • (weighted) £ gain
  • Average time interval between controller failures (ATBCF)
  • Dynamical output feedback
  • Exponential stability
  • Linear time-invariant (LTI) system
  • Piecewise Lyapunov function
  • Unavailability rate

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Stability and £ 2 gain analysis for discrete - Time LTI systems with controller failures . / Zhai, Guisheng; Chen, Xinkai; Lin, Hai.

In: IFAC Proceedings Volumes (IFAC-PapersOnline), Vol. 37, No. 11, 01.01.2004, p. 545-550.

Research output: Contribution to journalConference article

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