Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay

Guoping Liu, Yong He, Min Wu, Jin-hua She

Research output: Contribution to journalArticlepeer-review


This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.
Original languageEnglish
Pages (from-to)2372 - 2377
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number10
Publication statusPublished - 10 Nov 2008


  • time-varying delay
  • Discrete-time systems
  • linear matrix inequality (LMI)
  • output feedback
  • stabilization


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