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Authors
I. Penarrocha; A. Sala; R. Sanchis; P. Albertos

Digital Object Identifier (DOI)
10.3182/20050703-6-CZ-1902.00051

Page Numbers:
50-50

Index Terms
missing-data,random sampling,unconventional sampling,time-varying sampling periods,martingale convergence,linear matrix inequalities

Abstract
In this paper, the design of an output predictor in a system with random scarce sampling is addressed. A model based predictor that takes into account the past measured outputs is used, and a Lyapunov function of the estimation error is used for design purposes. The Lyapunov design problem becomes a feasibility problem over a set of linear matrix inequalities applying the Schur complement formula. Three different design approaches have been developed. Some examples show the performances of each approach.

References

[1] P. Albertos and G.C. Goodwin. Virtual sensors
    for control applications. Annual Reviews in
    Control, 26:101-112, 2002.
[2] P. Albertos, J. Salt, and J. Tornero. Dual rate
    adaptive control. Automatica, 31(7):1017-1030,
    1996.
[3] P. Albertos, R. Sanchis, and A. Sala. Output
    prediction under scarce data operation: Control
    applications. Automatica, 35:1671-1681, 1999.
[4] M. Araki. Recent development in digital control
    theory. Proc. 12th IFAC World Congr., 951-960
    (1993), 9.
[5] M. Araki and T. Hagiwara. Pole assignment by
    multirate data output feedback. International
    Journal of Control, 44(6):1661-1673, 1986.
[6] S. Boyd, L. Gaoui, E. Feron, and V. Balakrishnan.
     Linear Matrix Inequalities in Systems and
    Control Theory. SIAM. Philadelphia, 1994.
[7] P.P. Khargonekar, K. Poolla, and A. Tannenbaum.
     Robust control of linear time-invariant
    plants using periodic compensation. IEEE
    Trans. Automatic Control, 30:1088-1096, 1985.
[8] G.M. Kranc. Input-output analysis of multirate
    feedback systems. IRE Trans. Auto. Control,
    31(2):315-319, 1957.
[9] R.M. Palhares and P.L.D. Peres. Robust filtering
    with guaranteed energy-to-peak performance -
    an lmi approach. Automatica, 36:851-858, 2000.
[10] M.M. Rao. Foundations of stochastic Analysis.
     Academic Press, 1981.
[11] J. Salt, P. Albertos, and J. Tornero. Modelling
     of non-conventional sampled data systems. 3rd
     IEEE Control Applications Conference, 2:631-
     635, 1993.
[12] R. Sanchis. Control of Industrial Processes with
     Scarce Measurements. Doctoral Thesis, Universidad
      Politécnica de Valencia, Spain., 1999.
[13] R. Sanchis and P. Albertos. Recursive identification
      under scarce measurements. convergence
     analysis. Automatica, 38:535-544, 2002.
[14] J. Wang, C. Wang, and H. Gao. Robust H∞ filtering
      for lpv discrete-time state-delayed systems.
     Nature and Science, 2(2):36-45, 2004.
[15] Z. Wang, B. Huang, and H. Unbehauen. Robust
     H∞ observer design of linear state delayed systems
      with parametric uncertainty: the discrete-time
      case. Automatica, 35:1161-1167, 1999.
[16] L. Xie, L. Lu, D. Zhang, and H. Zhang. Improved
      robust H2 and H∞ filtering for uncertain
      discrete-time systems. Automatica, 40:873-
     880, 2004.
[17] S. Xu and T. Chen. Robust H∞ filtering for
     uncertain impulsive stochastic systems under
     sampled measurements. Automatica, 39:509-
     516, 2003.