Transactions on Control, Automation and Systems Engineering

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Discrete-Time Robust Guaranteed Cost Filtering for Convex Bounded Uncertain Systems With Time Delay

  • Kim, Jong-Hae (Division of Electronics, Information and Communication Engineering, Sunmoon University)
  • Published : 2002.12.01
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Abstract

In this paper, the guaranteed cost filtering design method for linear time delay systems with convex bounded uncertainties in discrete-time case is presented. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytotype less conservative than norm bounded parameter uncertainty. The main purpose is to design a stable filter which minimizes the guaranteed cost. The sufficient condition for the existence of filter, the guaranteed cost filter design method, and the upper bound of the guaranteed cost are proposed. Since the proposed sufficient conditions are LMI(linear matrix inequality) forms in terms of all finding variables, all solutions can be obtained simultaneously by means of powerful convex programming tools with global convergence assured. Finally, a numerical example is given to check the validity of the proposed method.

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References

  1. IEEE Trans. Automat. Control v.39 Optimal guaranteed cost control and filtering for uncertain linear systems I. R. Petersen;D. C. MeFarlane https://doi.org/10.1109/9.317138
  2. Proc. IEEE Conference on Decision and Control H$_2$ and H$_{\infty}$ robust filtering for convex bounded uncertain systems J. C. Geromel;M. C. Oliveira
  3. IEEE Transactions on Automatic Control v.36 Filtering and smoothing in H$_{\infty}$ setting K. M. Nagpal;P. P. Khargonekar https://doi.org/10.1109/9.67291
  4. International Journal of Robust and Nonlinear Control v.1 H$_{\infty}$ estimation for discrete time linear uncertain systems L. Xie;C. E. de Souza;M. Fu
  5. IEEE Transactions on Automatic Control v.42 no.10 Robust H$_2$/H$_{\infty}$ state estimation for discrete-time systems with error variance constraints Z. Wang;Z. Guo;H. Unbehauen https://doi.org/10.1109/9.633833
  6. Systems and Control Letters v.22 Robust Kalman filtering for uncertain systems L. Xie;Y. C. Soh https://doi.org/10.1016/0167-6911(94)90106-6
  7. Proc. American control Conference Robust H$_{\infty}$ filtering design with pole constraints for discrete-time systems: An LMI approach R. M. Palhares;P. L. D. Peres
  8. Automatica v.35 no.8 H$_{\infty}$ state feedback control for generalized continuous/discrete time delay system J. H. Kim;H. B. Park https://doi.org/10.1016/S0005-1098(99)00038-2
  9. IEEE Transactions on Signal Processing v.49 no.3 Robust H$_{\infty}$ filter design for uncertain linear systems with multiple time-varying state delays C. D. E. Souza;R. M. Palhares;P. L. D. Peres https://doi.org/10.1109/78.905882
  10. IEEE Transactions on Signal Processing v.49 no.4 Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation Z. Wang;K. J. Burnham https://doi.org/10.1109/78.912924
  11. Transactions on Control, Automation and System Engineering v.3 no.1 Robust guaranteed cost filtering for uncertain systems with time-varying delay via LMI approach J. H. Kim
  12. International Journal of Systems Science v.28 no.2 H$_{\infty}$ and H$_2$ guaranteed costs computation for uncertain linear systems R. M. Palhares;R. H. C. Takahashi;P. L. D. Peres https://doi.org/10.1080/00207729708929377
  13. SIAM Studies in Applied Mathematics Linear Matrix Inequalities in System and Control Theory S. Boyd;L. E. Ghaui;E. Feron;V. Balakrishnan
  14. LMI Control Toolbox P. Gahinet;A. Nemirovski;A. J. Laub;M. Chilali