Quantized H Control for Time-Delay Systems with Missing Measurements

  • Bo Shen
  • Zidong Wang
  • Huisheng Shu


In Chap. 2, the quantized H control problem is investigated for a class of nonlinear stochastic time-delay network-based systems with data missing, where two logarithmic quantizers are employed to quantize both the measured output and the input signals in the networked control systems. The data missing phenomena are modeled by introducing a diagonal matrix consisting of Bernoulli-distributed stochastic variables taking values 1 and 0, which means that the data from different sensors may be missing with different probabilities. Subsequently, by applying the method of sector-bound uncertainties, we obtain a sufficient condition under which the closed-loop system is stochastically stable and the controlled output satisfies the H performance constraint for all nonzero exogenous disturbances under zero initial condition. Then, we specialize the sufficient condition to some special cases with the hope that the simplified inequalities can be numerically checked more easily.


Control Output Network Control System Stochastic Stability Packet Dropout Nonlinear Stochastic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 2.
    Ball, J.A., Helton, J.W., Walker, M.L.: H control for nonlinear systems with output feedback. IEEE Trans. Autom. Control 38(4), 546–559 (1993) MathSciNetMATHCrossRefGoogle Scholar
  2. 25.
    Chesi, G., Garulli, A., Tesi, A., Vicino, A.: Solving quadratic distance problems: an lmi-based approach. IEEE Trans. Autom. Control 48(2), 200–212 (2003) MathSciNetCrossRefGoogle Scholar
  3. 26.
    Chesi, G., Garulli, A., Tesi, A., Vicino, A.: Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems. Springer, Berlin (2009) MATHCrossRefGoogle Scholar
  4. 28.
    Chow, M.Y., Tipsuwan, Y.: Gain scheduling of networked DC motor controllers based on QOS variations. IEEE Trans. Ind. Electron. 50(5), 936–943 (2003) CrossRefGoogle Scholar
  5. 34.
    Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State-space solutions to standard H 2 and H control problems. IEEE Trans. Autom. Control 34(8), 831–847 (1989) MathSciNetMATHCrossRefGoogle Scholar
  6. 39.
    Eustace, R.W., Woodyatt, B.A., Merrington, G.L., Runacres, A.: Fault signatures obtained from fault implant tests on an F404 engine. ASME Trans. J. Eng. Gas Turbines Power 116(1), 178–183 (1994) CrossRefGoogle Scholar
  7. 44.
    Fu, M., Xie, L.: The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50(11), 1689–1711 (2005) MathSciNetGoogle Scholar
  8. 61.
    Hong, S.: Scheduling algorithm of data sampling times in the integrated communication and control systems. IEEE Trans. Control Syst. Technol. 3, 225–231 (1995) CrossRefGoogle Scholar
  9. 72.
    Khasminskii, R.Z.: Stochastic Stability of Differential Equations. Khasminskiidhoff, Alphen aan den Rijn (1980) CrossRefGoogle Scholar
  10. 94.
    Mao, X.: Stochastic Differential Equations and Their Applications. Horwood Publisher, Chichester (1997) MATHGoogle Scholar
  11. 124.
    Skorohod, A.V.: Asymptotic Methods in the Theory of Stochastic Differential Equations, vol. 78. American Mathematical Society, Providence (2008) Google Scholar
  12. 139.
    Wang, Z., Liu, Y., Liu, X.: H filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities. Automatica 44(5), 1268–1277 (2008) MathSciNetCrossRefGoogle Scholar
  13. 141.
    Wang, Z., Yang, F., Ho, D.W.C., Liu, X.: Robust H control for networked systems with random packet losses. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 37(4), 916–924 (2007) CrossRefGoogle Scholar
  14. 151.
    Xie, L.: Output feedback H control of systems with parameter uncertainty. Int. J. Control 63(4), 741–750 (1996) MATHCrossRefGoogle Scholar
  15. 152.
    Xie, L., Soh, Y.C., de Souza, C.E.: Robust Kalman filtering for uncertain discrete-time systems. IEEE Trans. Autom. Control 39(6), 1310–1314 (1994) MATHCrossRefGoogle Scholar
  16. 158.
    Yang, F., Wang, Z., Ho, D.W.C., Gani, M.: Robust H control with missing measurements and time delays. IEEE Trans. Autom. Control 52(9), 1666–1672 (2007) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Bo Shen
    • 1
  • Zidong Wang
    • 2
  • Huisheng Shu
    • 1
  1. 1.School of Inform. Science & Technol.Donghua UniversityShanghaiChina, People’s Republic
  2. 2.Dept. of Information Systems & ComputingBrunel UniversityUxbridgeUK

Personalised recommendations