Stability analysis and failure tolerant control for discrete-time linear systems with controller failure

Weiming Xiang, Guisheng Zhai, Jian Xiao

Research output: Contribution to journalArticle

2 Citations (Scopus)


In this paper, the stability and failure tolerant control are investigated for discrete-time time-invariant linear systems with occasional controller failure due to physical or purposeful reason. By introducing the conceptions of minimal controller reliable time and maximal controller failure time, a novel time-varying piecewise quadratic Lyapunov function (TPQLF) approach is proposed to analyse the stability property of closed-loop system in presence of controller failure. The presented TPQLF method combines both merits of previous Lyapunov function based results such as common Lyapunov function and piecewise Lyapunov function approaches. Furthermore, based on TPQLF, the feasible region described by pairs of minimal controller reliable time and maximal controller failure time can be easily computed by an iterative algorithm. Then, on the basis of the analysis results, time-varying state feedback gains are formulated to construct failure tolerant controller. It is demonstrated that the time-varying structure of controller provides more failure tolerance capacity than time-invariant controller. Several numerical examples are given to illustrate our theoretic findings in this paper.

Original languageEnglish
Pages (from-to)559-570
Number of pages12
JournalInternational Journal of Control
Issue number3
Publication statusPublished - 2015 Mar 4



  • controller failure
  • exponential stability
  • failure tolerant control
  • time-varying piecewise quadratic Lyapunov function

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

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