A parameter-dependent approach to Robust H∞ filtering for time-delay systems

IEEE Transactions on Automatic Control

Volumn 53, Issue 10, 2008, Pages 2420-2425

  Gao, Huijun ^a   Meng, Xiangyu ^a   Chen, Tongwen ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

H filtering; Linear matrix inequality (LMI); Robust filtering; Time delay systems; Uncertain systems

Indexed keywords

DELAY CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; SIGNAL FILTERING AND PREDICTION; TIME DELAY; UNCERTAIN SYSTEMS;

ARBITRARY DEGREES; FILTERING PROBLEMS; LINEAR CONTINUOUS-TIME SYSTEMS; LINEAR MATRIX INEQUALITY (LMI); LINEAR MATRIXES; NUMERICAL EXAMPLES; PARAMETER UNCERTAINTIES; POLYNOMIAL PARAMETERS; ROBUST FILTERING; ROBUST H; TIME-DELAY SYSTEMS; TIME-VARYING DELAYS;

CONTINUOUS TIME SYSTEMS;

EID: 56549090186     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2007544     Document Type: Article

References (35)

1. ∞-minimum error state estimation of linear stationary processes," IEEE Trans. Automat. Control, vol. 35, no. 5, pp. 554-558, May 1990.
2. ∞ setting," IEEE Trans. Automat. Control, vol. 36, no. 2, pp. 152-166, Feb. 1991.
3. ∞ -norm estimation," IEEE Trans. Automat. Control, vol. 37, no. 6, pp. 828-831, Jun. 1992.
4. ∞ filtering for Markovian jump linear systems," Int. J. Syst. Sci., vol. 33, no. 11, pp. 909-915, 2002.
5. 2-L∞ filtering for a class of uncertain nonlinear time-delay systems," IEEE Trans. Automat. Control, vol. 48, no. 9, pp. 1661-1666, Sep. 2003.
6. ∞ filtering for uncertain discrete-time state-delayed systems," IEEE Trans. Signal Processing, vol. 49, no. 8, pp. 1696-1703, Aug. 2001.
7. ∞ observer design of linear state delayed systems with parametric uncertainty: The discrete-time case," Automatica, vol. 35, pp. 1161-1167, 1999.
8. E. Gershon, D. J. N. Limebeer, U. Shaked, and I. Yaesh, "Robust H & filtering of stationary continuous-time linear systems with stochastic uncertainties," IEEE Trans. Automat. Control, vol. 46, no. 11, pp. 1788-1793, Nov. 2001.
9. Z. Wang and K. J. Burnham, "Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation," IEEE Trans. Signal Processing, vol. 49, no. 4, pp. 794-804, Apr. 2001.
10. Z. Wang and B. Huang, "Robust filtering for linear systems with error variance constraints," IEEE Trans. Signal Processing, vol. 48, no. 8, pp. 2463-2467, Aug. 2000.
11. ∞ estimation for discrete-time linear uncertain systems," Int. J. Robust Nonlin. Control, vol. 1, pp. 111-123, 1991.
12. ∞ filter design for linear time delay systems," IEEE Trans. Signal Processing, vol. 49, no. 11, pp. 2839-2843, Nov. 2001.
13. H. Li and M. Fu, "A linear matrix inequality approach to robust H & filtering," IEEE Trans. Signal Processing, vol. 45, no. 9, pp. 2338-2350, Sep. 1997.
14. ∞ filter design with pole constraints for discrete-time systems," J. Franklin Inst., vol. 337, pp. 713-723, 2000.
15. 2 and H & filtering for uncertain linear systems," Automatica, vol. 42, pp. 1919-1926, 2006.
16. ∞ filtering of linear systems with time-varying delay," IEEE Trans. Automat. Control, vol. 48, no. 1, pp. 159-165, Jan. 2003.
17. ∞ filtering foruncer-tain discrete-time systems," Automatica, vol. 40, pp. 873-880, 2004.
18. ∞ performance," Proc. Inst. Elect. Eng. D vol. 152, no. 5, pp. 531-537, 2005.
19. ∞ filter design for systems with polytope-bounded uncertainty," IEEE Trans. Signal Processing, vol. 54, no. 9, pp. 3620-3626, Sep. 2006.
20. M. Sato, "Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions," Automatica, vol. 42, no. 11, pp. 2017-2023, 2006.
21. 2 filtering for uncertain systems with multiple time-varying state delays," Signal Processing, vol. 87, no. 4, pp. 709-724, 2007.
22. ∞ filter design for uncertain linear systems with multiple time-varying state delays," IEEE Trans. Signal Processing, vol. 49, no. 3, pp. 569-576, Mar. 2001.
23. ∞ filtering for uncertain discrete-time state-delayed systems," IEEE Trans. Signal Processing, vol. 52, no. 6, pp. 1631-1640, Jun. 2004.
24. R. C. L. F. Oliveira and P. L. D. Peres, "LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions," Syst. Control Lett., vol. 55, no. 1, pp. 52-61, 2006.
25. D. Henrion and J. B. Lasserre, "Convergent relaxations of polynomial matrix inequalities and static output feedback," IEEE Trans. Automat. Control, vol. 51, no. 2, pp. 192-202, Feb. 2006.
26. G. Chesi, "On the gap between positive polynomials and sos of polynomials," IEEE Trans. Automat. Control, vol. 52, no. 6, pp. 1066-1072, Jun. 2007.
27. M. C. de Oliveira, J. Bernussou, and J. C. Geromel, "A new discrete-time robust stability condition," Syst. Control Lett., vol. 37, pp. 261-265, 1999.
28. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Homogeneous Lyapunov functions for systems with structured uncertainties," Automatica, vol. 39, pp. 1027-1035, 2003.
29. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions," Automatica, vol. 43, pp. 309-316, 2007.
30. A. Papachristodoulou, "Scalable Analysis of Nonlinear Systems Using Convex Optimization," Ph.D. dissertation, Control Dynamical Syst., California Inst. Technology, Pasadena, 2005.
31. K. Barbosa, C. E. de Souza, and A. Trofino, "Robust H2 filtering discrete-time uncertain linear systems using parameters-dependent lyapunov functions," in Proc. Amer. Control Conf., Anchorage, AK, 2002, pp. 3224-3229.
32. ∞ filtering for discrete-time linear systems with uncertain time-varying parameters," IEEE Trans. Signal Processing, vol. 54, no. 6, pp. 2110-2118, Jun. 2006.
33. ∞ filtering for a class of uncertain linear systems with time-varying delay," Automatica, vol. 44, no. 1, pp. 157-166, 2008.
34. Y. He, Q. Wang, Q. Lin, and M. Wu, "Delay-range-dependent stability for systems with time-varying delay," Automatica, vol. 43, pp. 371-376, 2007.
35. S. Xu and J. Lam, "Improved delay-dependent stability criteria for time-delay systems," IEEE Trans. Automat. Control, vol. 50, no. 3, pp. 384-387, Mar. 2005.