Generalized two-dimensional Kalman-Yakubovich-Popov lemma for discrete roesser model

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 55, Issue 10, 2008, Pages 3223-3233

  Yang, Ran ^a   Xie, Lihua ^b   Zhang, Cishen ^b  

^a SUN YAT SEN UNIVERSITY   (China)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

2 D systems; Bounded and positive realness; Kalman Yakubovich Popov (KYP) lemma; Roesser model; Two dimensional (2 D) digital filters

Indexed keywords

COMPUTATION THEORY; DIGITAL FILTERS; KALMAN FILTERS; LINEAR MATRIX INEQUALITIES;

2-D SYSTEMS; BOUNDED AND POSITIVE REALNESS; KALMAN-YAKUBOVICH-POPOV LEMMA; ROESSER MODELS; TWO-DIMENSIONAL (2-D) DIGITAL FILTERS;

FREQUENCY DOMAIN ANALYSIS;

EID: 57149134394     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.923284     Document Type: Article

References (32)

1. R. W. Aldhaheri, "Design of 2-D linear phrase digital filters using schur decomposition and symmetries," Multidimensional Syst. Signal Process., vol. 15, no. 1, pp. 65-81, 2004.
2. B. D. O. Anderson, P. Agathoklis, E. I. Jury, and M. Mansuor, "Stability and the matrix Lyapunov equation for discrete 2-dimensional systems," IEEE Trans. Circuits Syst., vol. CAS-33, no. 3, pp. 261-267, Mar. 1986.
3. A. Antoniou and W. S. Lu, "Design of two-dimwnsional digital filters by using the singular value decomposition," IEEE Trans. Circuits Syst. vol. 34, no. 10, pp. 1191-1198, Oct. 1987.
4. T. Bose, M. Chen, and R. Thamvichai, "Stability of the 2-D Givone-Roesser model with periodic coefficients," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 3, pp. 566-578, Mar. 2007.
5. C. Charalambous, "The performance of an algorithm for minimax design of two-dimensional linear phase FIR digital filters," IEEE Trans. Circuits Syst., vol. CAS-33, no. 3, pp. 261-267, Mar. 1985.
6. T. B. Deng and M. Kawamata, "Frequency-domain design of 2-D digital fitlers using singular value decomposition," IEEE Trans. Circuits Syst., vol. 38, no. 10, pp. 1225-1228, Oct. 1991.
7. T. B. Deng, E. Saito, and E. Okamoto, "Efficient design of SVD-based 2-D digital filters using specification symmetry and order-selecting criterion," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 217-226, Feb. 2003.
8. C. Du and L. Xie, H∞ Control and Filtering of Two-Dimensional Systems. Berlin, Germany: Springer-Verlag, 2002.
9. D. Dudgeon and R. Mersereau, Multidimensional Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
10. K. Galkowski, J. Lam, S. Xu, and Z. Lin, "LMI approach to state-feedback stabilization of multidimensional systems," Int. J. Control, vol. 76, pp. 1428-1436, 2003.
11. D. B. Harris and R. M. Mersereau, "A comparison of algorithms for minimax design of two-dimensional linear phrase FIR digital filters," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-25, no. 6, pp. 492-500, Dec. 1977.
12. T. Huang, "Two-dimensional windows," IEEE Trans. Audio Electroacoust., vol. AE-20, no. 1, pp. 88-89, Mar. 1972.
13. T. Iwasaki and S. Hara, "Generalized KYP lemma: Unified frequency domain inequalities with design applications," IEEE Trans. Autom. Control, vol. 50, no. 1, pp. 41-59, 2005.
14. T. Iwasaki, G. Meinsma, and M. Fu, "Generalized S-procedure and finite frequency KYP lemma," Math. Problems Eng., vol. 6, pp. 305-320, 2000.
15. T. Kaczorek, Two-Dimensional Linear Systems. Berlin, Germany: Springer-Verlag, 1985.
16. R. E. Kalman, "Lyapunov functions for the problem of lur'e in automatic control," in Proc. Nat. Acad. Sci., 1963, vol. 49, pp. 201-205.
17. R. A. Kennedy, B. D. O. Anderson, and R. R. Bitmead, "Channels leading to rapid error recovery for decision feedback equalizers: Passivity analysis," in Proc. 27th IEEE Conf. Decision Contr., Austin, TX, 1998, pp. 2402-2407.
18. J. E. Kurek, "Stability of positive 2-D system described by the Roesser model," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 4, pp. 531-533, Apr. 2002.
19. C. Li and M. S. Fadali, "Optimal control of 2-D systems," IEEE Trans. Autom. Control, vol. 36, no. 2, pp. 223-228, Feb. 1991.
20. H. C. Lu and K. H. Yeh, "2-D FIR filter design using least square error with scaling free McClellan transformation," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 47, no. 7, pp. 1104-1107, Jul. 2000.
21. W. S. Lu, H. P. Wang, and A. Antoniou, "Design of two-dimensional FIR digital filters by using the singular value decomposition," IEEE Trans. Circuits Syst., vol. 37, no. 1, pp. 35-46, Jan. 1990.
22. R. M. Mersereau, "The design of arbitrary 2-D zero phase FIR filters using transformations," IEEE Trans. Circuits Syst., vol. CAS-27, no. 2, pp. 142-144, Feb. 1980.
23. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing Englewood Cliffs, NJ: Prentice-Hall, 1989.
24. A. Rantzer, "On the Kalman-Yakubovich-Popov Lemma," Syst. Control Lett., vol. 28, no. 1, pp. 7-10, Jun. 1996.
25. R. P. Roesser, "A discrete state-space model for linear image processing," IEEE Trans. Autom. Control, vol. 20, no. 1, pp. 1-10, Jan. 1975.
26. E. Rogers, K. Galkowski, A. Gramacki, J. Gramacki, and D. H. Owens, "Stability and controllability of a class of 2-D linear systems with dynamic boundary conditions," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 181-195, Jan. 2002.
27. T. C. Speake and R. M. Mersereau, "A note on the use of windows for two-dimensional FIR filter design," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-29, no. 1, pp. 125-127, Feb. 1981.
28. L. Xie, M. Fu, and H. Li, "Passivity analysis and passification for uncertain signal processing systems," IEEE Trans. Signal Process. vol. 46, no. 9, pp. 2394-2403, Sep. 1998.
29. L. Xu, O. Saito, and K. Abe, "Output feedback stabilizability and stabilization algorithms for 2-D systems," Multidimensional Syst. Signal Process., vol. 5, no. 1, pp. 41-60, Jan. 1994.
30. S. Xu, J. Lam, Z. Lin, and K. Galkowski, "Positive real control for uncertain two-dimensional systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 11, pp. 1659-1666, Nov. 2002.
31. S. Xu, J. Lam, Z. Lin, K. Galkowski, W. Paszke, B. Sulikowsk, E. Rogers, and D. Owens, "Positive real control of two-dimensional systems: Roesser models and linear repetitive processes," Int. J. Control, vol. 76, no. 11, pp. 1047-1058, Jul. 2003.
32. S. Xu, J. Lam, Y. Zou, Z. Lin, and W. Paszke J, "Robust H∞ filtering for uncertain 2-D continuous systems," IEEE Trans. Signal Process., vol. 53, no. 5, pp. 1731-1758, May 2005.