access icon free Stabilisation of non-uniformly sampled systems via dynamic output-feedback control

Stabilisation of sampled-data systems with time-varying and uncertain sampling periods via dynamic output-feedback controllers is considered. Extending the existing discrete-time approaches to the more general setup of output-feedback control, sufficient linear matrix inequalities conditions are developed for the design of linear, constant-parameter controllers. The applicability of the proposed design method is demonstrated through numerical examples, which also indicate improvement with regards to the other approaches.

Inspec keywords: discrete time systems; uncertain systems; sampled data systems; time-varying systems; stability; linear matrix inequalities; feedback; control system synthesis; sampling methods

Other keywords: dynamic output-feedback controllers; linear matrix inequalities conditions; sampled-data system stabilisation; constant-parameter controller design; nonuniformly sampled system stabilisation; time-varying sampling periods; discrete-time approaches; uncertain sampling periods; linear controller design

Subjects: Linear algebra (numerical analysis); Stability in control theory; Time-varying control systems; Discrete control systems; Other topics in statistics; Control system analysis and synthesis methods

References

    1. 1)
      • 5. Walsh, G.C., Ye, H., Bushnell, L.: ‘Stability analysis of networked control systems’, IEEE Trans. Control Syst. Technol., 2002, 10, (3), pp. 438446.
    2. 2)
      • 2. Hristu-Varsakelis, D.W.S.L., (Eds.): ‘Handbook of networked and embedded control systems’ (Birkhäuser, 2005).
    3. 3)
      • 7. Mirkin, L.: ‘Some remarks on the use of time-varying delay to model sample-and-hold circuits’, IEEE Trans. Autom. Control, 2007, 52, (6), pp. 11091112.
    4. 4)
      • 17. Naghshtabrizi, P., Hespanha, J., Teel, A.: ‘On the robust stability and stabilization of sampled-data systems: a hybrid system approach’, 45th IEEE Conf. on Decision and Control, December 2006, pp. 48734878.
    5. 5)
      • 10. Suh, Y.S.: ‘Stability and stabilization of nonuniform sampling systems’, Automatica, 2008, 44, (12), pp. 32223226.
    6. 6)
      • 12. Fujioka, H., Nakai, T.: ‘Stabilizing systems with aperiodic sampling-and-hold devices: state feedback case’, IET Control Theory Appl., 2010, 4, pp. 262272.
    7. 7)
      • 8. Fujioka, H.: ‘Stability analysis of systems with aperiodic sample-and-hold devices’, Automatica, 2009, 45, (3), pp. 771775.
    8. 8)
      • 14. Hetel, L., Cloosterman, M., van de Wouw, N., Heemels, W., Daafouz, J., Nijmeijer, H.: ‘Comparison of stability characterisations for networked control systems’, 48th IEEE Conf. on Decision and Control, 28th Chinese Control Conf., December 2009, pp. 79117916.
    9. 9)
      • 13. Fujioka, H.: ‘Stability analysis for a class of networked/embedded control systems: output feedback case’, 17th IFAC World Congress, 2008, pp. 42104215.
    10. 10)
      • 25. Hetel, L., Daafouz, J., Iung, C.: ‘Analysis and control of LTI and switched systems in digital loops via an event-based modelling’, Int. J. Control, 2008, 81, (7), pp. 11251138.
    11. 11)
      • 19. Hu, S., Yue, D., Du, Z., Liu, J.: ‘Reliable ℋ non-uniform sampling tracking control for continuous-time non-linear systems with stochastic actuator faults’, IET Control Theory Appl., 2012, 6, (1), pp. 120129.
    12. 12)
      • 6. Fridman, E., Seuret, A., Richard, J.-P.: ‘Robust sampled-data stabilization of linear systems: an input delay approach’, Automatica, 2004, 40, (8), pp. 14411446.
    13. 13)
      • 20. Yuz, J., Alfaro, J., Agüero, J., Goodwin, G.: ‘Identification of continuous-time state-space models from non-uniform fast-sampled data’, IET Control Theory Appl., 2011, 5, (7), pp. 842855.
    14. 14)
      • 4. Zhang, W., Branicky, M.: ‘Stability of networked control systems with time-varying transmission period’, Conf. Communication, Control and Computing, 2001.
    15. 15)
      • 23. Loan, C.V.: ‘The sensitivity of the matrix exponential’, SIAM J. Numer. Anal., 1977, 14, pp. 971981.
    16. 16)
      • 21. Naghshtabrizi, P., Hespanha, J.: ‘Designing an observer-based controller for a network control system’, Proc. 44th IEEE CDC and European Control Conf., 2005, pp. 848853.
    17. 17)
      • 9. Fridman, E.: ‘A refined input delay approach to sampled-data control’, Automatica, 2010, 46, (2), pp. 421427.
    18. 18)
      • 26. Löfberg, J.: ‘Yalmip: a toolbox for modeling and optimization in MATLAB’, Proc. Computer-Aided Control System Design, 2004.
    19. 19)
      • 27. Fujioka, H., Oishi, Y.: ‘A switched Lyapunov function approach to stability analysis of non-uniformly sampled-data systems with robust LMI techniques’, Proc. Eighth IEEE Asian Control Conf., 2011, pp. 14871491.
    20. 20)
      • 22. Mustafa, G., Chen, T.: ‘ filtering for nonuniformly sampled systems: A markovian jump systems approach’, Syst. Control Lett., 2011, 60, (10), pp. 871876.
    21. 21)
      • 24. Scherer, C.: ‘Theory of robust control’. Course notes, Delft University of Technology, The Netherlands, 2001.
    22. 22)
      • 3. Kalman, R.E.: ‘Analysis and synthesis of linear dynamical systems operating on randomly sampled data’. PhD thesis, Columbia University, New York, NY, 1957.
    23. 23)
      • 11. Fujioka, H.: ‘A discrete-time approach to stability analysis of systems with aperiodic sample-and-hold devices’, IEEE Trans. Autom. Control, 2009, 54, (10), pp. 24402445.
    24. 24)
      • 1. Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: ‘A survey of recent results in networked control systems’, Proc. IEEE, 2007, 95, (1), pp. 138162.
    25. 25)
      • 16. Oishi, Y., Fujioka, H.: ‘Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities’, Automatica, 2010, 46, (8), pp. 13271333.
    26. 26)
      • 15. Hetel, L., Kruszewski, A., Perruquetti, W., Richard, J.: ‘Discrete and intersample analysis of systems with aperiodic sampling’, IEEE Trans. Autom. Control, 2011, 56, (7), pp. 16961701.
    27. 27)
      • 18. Geromel, J.C., Korogui, R.H., Bernussou, J.: ‘2 and ℋ robust output feedback control for continuous time polytopic systems’, IET Control Theory Appl., 2007, 1, (5), pp. 15411549.
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