Robust H∞ filtering for uncertain 2-D continuous systems

IEEE Transactions on Signal Processing

Volumn 53, Issue 5, 2005, Pages 1731-1738

  Xu, Shengyuan ^a   Lam, James ^b   Zou, Yun ^a   Lin, Zhiping ^c   Paszke, Wojciech ^d  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^d UNIVERSITY OF ZIELONA GÓRA   (Poland)

Author keywords

2 D continuous systems; H filtering; Linear matrix inequality; Uncertain systems

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; DIGITAL FILTERS; ESTIMATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; STATE SPACE METHODS; TRANSFER FUNCTIONS; UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITY; TWO DIMENSIONAL CONTINUOUS SYSTEMS;

SIGNAL FILTERING AND PREDICTION;

EID: 18844441816     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2005.845464     Document Type: Article

References (27)

1. B. D. O. Anderson and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
2. S. Bittanti and F. A. Cuzzola, "Continuous-time periodic H∞ filtering via LMI," Eur. J. Control, vol. 7, pp. 2-16, 2001.
3. 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.
4. R. D'Andrea and G. E. Dullerud, "Distributed control design for spatially interconnected systems," IEEE Trans. Autom. Control, vol. 48, no. 9, pp. 1478-1495, Sep. 2003.
5. C. E. de Souza, L. Xie, and Y. Wang, " H∞ filtering for a class of uncertain nonlinear systems," Syst. Control Lett., vol. 20, pp. 419-426, 1993.
6. C. Du and L. Xie, "Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach," IEEE Trans. Circuits Syst. I-Funda. Theory Applicat., vol. 46, no. 11, pp. 1371-1374, Nov. 1999.
7. C. Du and L. Xie, H∞ Control and Filtering of Two-Dimensional Systems. Heidelberg, Germany: Springer-Verlag, 2002.
8. E. Fridman and U. Shaked, "A new H∞ filter design for linear time delay systems," IEEE Trans. Signal Process., vol. 49, no. 11, pp. 2839-2843, Nov. 2001.
9. K. Galkowski, "LMI based stability analysis for 2D continuous systems," in Proc. 9th IEEE Int. Conf. Electron., Circuits Syst., Dubrovnik, Croatia, Sep. 2002, pp. 923-926.
10. M. J. Grimble and A. El Sayed, "Solution of the H∞ optimal linear filtering problem for discrete-time systems," IEEE Trans. Acoust., Speech. Signal Process., vol. 38, no. 7, pp. 1092-1104, Jul. 1990.
11. W. M. Haddad and D. S. Bernstein, "Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory," Int. J. Robust Nonlinear Control, vol. 3, pp. 313-339, 1993.
12. S. H. Jin and J. B. Park, "Robust H∞ filtering for polytopic uncertain systems via convex optimization," Proc. Inst. Elect. Eng. - Control Theory Appl., vol. 148, pp. 55-59, 2001.
13. T. Kaczorek, Two-Dimensional Linear Systems. Berlin, Germany: Springer-Verlag, 1985.
14. T. Kaczoreck, "Local controllability and minimum energy control of continuous 2-D linear systems with variable coeffcients," Multidimensional Syst. Signal Process., vol. 6, pp. 69-75, 1995.
15. P. P. Khargonekar, I. R. Petersen, and K. Zhou, "Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control theory," IEEE Trans. Autom. Control, vol. 35, no. 3, pp. 356-361, Mar. 1990.
16. J. H. Lodge and M. M. Fahmy, "The bilinear transformation of two-dimensional state-space systems," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-30, no. 3, pp. 500-502, Jun. 1982.
17. N. E. Mastorakis, D. H. Owens, and A. E. Venetsanopoulos, "Stability margin of two-dimensional continuous systems," IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3591-3594, Dec. 2000.
18. N. E. Mastorakis and M. Swamy, "A new method for computing the stability margin of two-dimensional continuous systems," IEEE Trans. Circuits Syst. I-Funda. Theory Applicat., vol. 49, no. 6, pp. 869-872, Jun. 2002.
19. K. M. Nagpal and P. P. Khargonekar, "Filtering and smoothing in an H ∞ setting," IEEE Trans. Autom. Control, vol. 36, no. 2, pp. 152-166, Feb. 1991.
20. M. S. Piekarski, "Algebraic characterization of matrices whose multi-variable characteristic polynomial is Hermitzian," in Proc. Int. Symp. Operator Theory, Lubbock, TX, 1977, pp. 121-126.
21. U. Shaked, "H ∞ minimum error state estimation of linear stationary processes," IEEE Trans. Autom. Control, vol. 35, no. 5, pp. 554-558, May 1990.
22. K. Takaba and T. Katayama, "Discrete-time H∞ algebraic Riccati equation and parametrization of all H∞, filters," Int. J. Control, vol. 64, pp. 1129-1149, 1996.
23. 2/H∞ filtering of 2-D systems," IEEE Trans. Signal Process., vol. 50, no. 7, pp. 1759-1771, Jul. 2002.
24. C. Xiao, P. Agathoklis, and D. J. Hill, "On the positive definite solutions to the 2-D continuous-time Lyapunov equation," Multidimensional Syst. Signal Process., vol. 8, pp. 315-333, 1997.
25. L. Xie, C. Du, C. Zhang, and Y. C. Soh, "H∞ deconvolution filtering of 2-D digital systems," IEEE Trans. Signal Process., vol. 50, no. 9, pp. 2319-2332, Sep. 2002.
26. S. Xu, T. Chen, and J. Lam, "Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays," IEEE Trans. Autom. Control, vol. 48, no. 5, pp. 900-907, May 2003.
27. S. Xu and P. Van Dooren, "Robust H∞ filtering for a class of nonlinear systems with state delay and parameter uncertainty," Int. J. Control, vol. 75, pp. 766-774, 2002.