Control of LPV Time-Delay Systems

  • Corentin BriatEmail author
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 3)


This chapter pertains of the control of linear parameter-varying time-delay systems in the framework of parameter-dependent differential equations and Lyapunov-Krasovskii functionals. State-feedback and output-feedback controllers are considered both in the memoryless and with-memory cases. Controllers with approximate memory, which implement a different delay than the one in the system, are also introduced and shown to generalize the concepts of memoryless controllers and controllers with exact memory. Some examples with simulations are given for illustration.


  1. 1.
    Y. Orlov, L. Belkoura, J.-P. Richard, M. Dambrine, Adaptive identification of linear time-delay systems. International Journal of Robust and Nonlinear Control 13(9), 857–872 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    S. Drakunov, S. Perruquetti, J.P. Richard, L. Belkoura, Delay identification in time-delay systems using variable structure control. Annual Reviews in Control 30(2), 143–158 (2006)CrossRefGoogle Scholar
  3. 3.
    L. Belkoura, J.P. Richard, M. Fliess, Real time identification of time-delay systems (In IFAC Workshop on Time-Delay Systems, Nantes, France, 2007)Google Scholar
  4. 4.
    L. Belkoura, J.P. Richard, M. Fliess, A convolution approach for delay systems identification (In IFAC World Congress, Seoul, South Korea, 2008)Google Scholar
  5. 5.
    F. Wu, K.M. Grigoriadis, LPV systems with parameter-varying time delays: analysis and control. Automatica 37, 221–229 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    F. Zhang and K. M. Grigoriadis. Delay-dependent stability analysis and \({\cal {H}}_\infty \) control for state-delayed LPV system. In Mediterranean Conference on Control and Automation, pages 1532–1537, 2005.Google Scholar
  7. 7.
    L. El-Ghaoui, F. Oustry, M. Ait, Rami. A Cone Complementary linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control 42, 1171–1176 (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    H.H. Choi, M.J. Chung, Observer-based \({\cal {H}}_{\infty }\) controller design for state delayed linear systems. Automatica 32(7), 1073–1075 (1996)Google Scholar
  9. 9.
    H.H. Choi, M.J. Chung, Robust observer-based \({\cal {H}}_{\infty }\) controller design for linear uncertain time-delay systems. Automatica 33(9), 1749–1752 (1997)Google Scholar
  10. 10.
    O. Sename and C. Briat. Observer-based \({\cal {H}}_\infty \) control for time-delay systems: a new LMI solution. In 6th IFAC Workshop on Time Delay Systems, L’Aquila, Italy, 2006.Google Scholar
  11. 11.
    O. Sename, Is a mixed design of observer-controllers for time-delay systems interesting ? Asian Journal of Control 9(2), 180–189 (2007)CrossRefMathSciNetGoogle Scholar
  12. 12.
    K. Tan, K.M. Grigoriadis, F. Wu, \({\cal {H}}_{\infty } \) and \({\cal {L}}_2\)-to-\({\cal {L}}_{\infty } \) gain control of linear parameter varying systems with parameter varying delays. Control Theory and Applications 150, 509–517 (2003)Google Scholar
  13. 13.
    C. Briat. Robust Control and Observation of LPV Time-Delay Systems. Grenoble Institute of Technology (2008)
  14. 14.
    C.W. Scherer, P. Gahinet, M. Chilali, Multiobjective output-feedback control via LMI optimization. IEEE Transaction on Automatic Control 42(7), 896–911 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    C. W. Scherer and S. Weiland. Linear matrix inequalities in control. Lecture Notes; Available online, 2005
  16. 16.
    J. de Caigny, J.F. Camino, R.C.L.F. Oliveira, P. L.D. Peres, and J. Swevers. Gain-scheduled dynamic output feedback control for discrete-time LPV systems. International Journal of Robust and Nonlinear Control 22, 535–558 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    C. Briat, O. Sename, J.-F. Lafay, Memory resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays. Syst. Control Lett. 59, 451–459 (2010)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Biosystems Science and EngineeringSwiss Federal Institute of Technology–ZürichBaselSwitzerland

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