Multiobjective filter design for uncertain stochastic time-delay systems

IEEE Transactions on Automatic Control

Volumn 49, Issue 1, 2004, Pages 149-154

  Subramanian, Ananth ^a   Sayed, Ali H ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Exponential stability; Kalman filter; Linear matrix inequality; Robust filter; Stochastic uncertainties; Time delay systems

Indexed keywords

DELAY CONTROL SYSTEMS; ERROR ANALYSIS; KALMAN FILTERING; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); STOCHASTIC CONTROL SYSTEMS; TIME VARYING CONTROL SYSTEMS; UNCERTAIN SYSTEMS;

BOUNDED ERROR VARIANCE; EXPONENTIALLY STABLE FILTERS; LINEAR MATRIX INEQUALITY; LINEAR STABLE FILTERS; MULTIOBJECTIVE FILTER; STOCHASTIC UNCERTAINTIES;

CONTROL SYSTEM SYNTHESIS;

EID: 0742321617     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.821422     Document Type: Article

References (25)

1. T. Kailath, A.-H. Sayed, and B. Hassibi, Linear Estimation. Upper Saddle River, NJ: Prentice-Hall, 2000.
2. I. R. Petersen and A. V. Savkin, Robust Kalman Filtering for Signals and Systems With Large Uncertainties. Boston, MA: Birkhaüser, 1999.
3. L. Xie, Y. C. Soh, and C. E. De Souza, "Robust Kalman filtering for uncertain discrete-time systems," IEEE Trans. Automat. Contr. vol. 39, pp. 1310-1314, June 1994.
4. P. Bolzern, P. Colaneri, and G. De Nicolao, "Optimal design of robust predictors for linear discrete-time systems," Syst. Control Lett., vol. 26, pp. 25-31, 1995.
5. W. M. Haddad and D. S. Bernstein, "The optimal projection equations for reduced-order, discrete-time state estimation for linear systems with multiplicative white noise," Syst. Control Lett., vol. 8, pp. 381-388, 1987.
6. L. Xie, C. E. De Souza, and M. Fu, "H∞ estimation for discrete-time linear uncertain systems," Int. J. Robust Nonlinear Control, vol. 1, pp. 111-123, 1991.
7. D. P. Bertsekas and I. B. Rhodes, "Recursive state estimation for a set-membership description of uncertainty," IEEE Trans. Automat. Contr., vol. AC-16, pp. 117-128, Apr. 1971.
8. A. Garulli, A. Vicino, and G. Zappa, "Conditional central algorithms for worst case set-membership identification and filtering," IEEE Trans. Automat. Contr., vol. 45, pp. 14-23, Jan. 2000.
9. F. Yang, Z. Wang, and Y. S. Hung, "Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises," IEEE Trans. Automat. Contr., vol. 47, pp. 179-183, July 2002.
10. F. Wang and V. Balakrishnan, "Robust Kalman filtering for linear time varying systems with stochastic parametric uncertainties," IEEE Trans. Signal Processing, vol. 50, pp. 803-813, Apr. 2002.
11. J. C. Geromel, "Optimal linear filtering under parameter uncertainty," IEEE Trans. Signal Processing, vol. 47, pp. 168-175, Jan. 1999.
12. U. Shaked and E. De Souza, "Robust minimum variance filtering," IEEE Trans. Signal Processing, vol. 43, pp. 2474-2483, Nov. 1995.
13. A. H. Sayed, "A framework for state space estimation with uncertain models," IEEE Trans. Automat. Contr., vol. 46, pp. 998-1013, July 2001.
14. C. T. Leondes and J. O. Earson, "A minimax filter for systems with large parametric uncertainties," IEEE Trans. Automat. Contr., vol. AC-17, pp. 266-268, Apr. 1972.
15. P. P. Khargonekar and K. M. Nagpal, "Filtering and smoothing in an H∞ setting," IEEE Trans. Automat. Contr., vol. 36, pp. 151-166, Feb. 1991.
16. H. Kushner, Stochastic Stability and Control. New York: Academic, 1967
17. P. P. Khargonekar, I. R. Petersen, and K. Zhou, "Robust stabilization of uncertain linear systems: Quadratic stability and H∞ control theory," IEEE Trans. Automat. Contr. vol. 35, pp. 356-361, Mar. 1990.
18. E. K. Boukas and Z. K. Liu, "Robust H∞ control of discrete time Markovian jump linear systems with mode-dependent delays," IEEE Trans. Automat. Contr., vol. 46, pp. 1918-1924, Dec. 2001.
19. T. J. Tarn and Y. Rasis, "Observers for nonlinear stochastic systems," IEEE Tran. Automat. Contr., vol. AC-21, pp. 441-447, June 1976.
20. R. G. Agniel and E. I. Jury, "Almost sure boundedness of randomly sampled systems," SIAM J. Control, vol. 9, pp. 372-383, 1971.
21. M. Loeve, Probability Theory. New York: Springer-Verlag, 1977, vol. 1.
22. A. Subramanian and A. H. Sayed, "Robust exponential filtering for discrete-time uncertain systems," in Proc. Conf. Decision Control, Vol. 1, Las Vegas, NV, 2002, pp. 1023-1027.
23. ____, "A robust power control algorithm for state-delayed wireless networks," 2004, submitted for publication.
24. ____, "A minimum variance power update algorithm for wireless networks," presented at the Proc. Vehicular Technology Conference, Orlando, FL, Oct. 2003.
25. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, ser. SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM. 1994.