Robust finite frequency H∞ filtering for uncertain 2-D systems: The FM model case

Automatica

Volumn 49, Issue 8, 2013, Pages 2446-2452

  Li, Xianwei ^a   Gao, Huijun ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b BOHAI UNIVERSITY   (China)

Author keywords

Finite frequency (FF); Fornasini Marchesini (FM) model; Robust H filtering; Two dimensional (2 D) systems

Indexed keywords

DELAY CONTROL SYSTEMS; DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; LIFE SUPPORT SYSTEMS (SPACECRAFT); LINEAR MATRIX INEQUALITIES;

DISCRETE - TIME SYSTEMS; FINITE FREQUENCIES; FORNASINI MARCHESINI LOCAL STATE SPACES; FORNASINI-MARCHESINI MODEL; MODEL TRANSFORMATION; ROBUST H; TWO DIMENSIONAL (2 D); TWO-DIMENSIONAL (2D) SYSTEMS;

UNCERTAINTY ANALYSIS;

EID: 84882453767     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2013.04.014     Document Type: Article

References (25)

1. Basin, M., Elvira-Ceja, S. & Sanchez, E. N. (2012). Mean-square H∞ filtering for stochastic systems: application to a 2DOF helicopter. Signal Processing, 92, 801-806.
2. Boyd, S., El Ghaoui, L., Feron, E. & Balakrishnan, V. (1994). Linear matrix inequalities in systems and control theory. Philadelphia, PA: SIAM.
3. Chen, S. F. & Fong, I. K. (2006). Robust filtering for 2-D state-delayed systems with NFT uncertainties. IEEE Transactions on Signal Processing, 54, 274-285.
4. de Souza, C. E., Xie, L. & Coutinho, D. F. (2010). Robust filtering for 2-D discretetime linear systems with convex-bounded parameter uncertainty. Automatica, 46, 673-681.
5. Du, C. & Xie, L. (2002). H∞ control and filtering of two-dimensional systems. Berlin, Heidelberg: Springer-Verlag.
6. Fornasini, E. & Marchesini, G. (1978). Doubly indexed dynamical systems: statespace models and structual properties. Mathematical Systems Theory, 12, 59-72.
7. Gahinet, P. & Apkarian, P. (1994). A linear matrix inequality approach to H∞ control. International Journal of Robust and Nonlinear Control, 4, 421-448.
8. Gao, H. & Li, X. (2011). H∞ filtering for discrete-time state-delayed systems with finite frequency specifications. IEEE Transactions on Automatic Control, 56, 2935-2941.
9. Gonçalves, E. N., Palhares, R. M. & Takahashi, R. H. C. (2006). H2/H∞ filter design for systems with polytope-bounded uncertainty. IEEE Transactions on Signal Processing, 54, 3620-3626.
10. Hinamoto, T. (1997). Stability of 2-D discrete systems described by the Fornasini-Marchesini second model. IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications, 44, 254-257.
11. Hladowski, L., Galkowski, K., Cai, Z., Rogers, E., Freeman, C. T. & Lewin, P. L. (2011). A 2D systems approach to iterative learning control for discrete linear processes with zero Markov parameters. International Journal of Control, 84, 1246-1262.
12. Hoang, N. T., Tuan, H. D., Nguyen, T. Q. & Hosoe, S. (2005). Robust mixed generalized H2/H∞ filtering of 2-D nonlinear fractional transformation systems. IEEE Transactions on Signal Processing, 53, 4697-4706.
13. Li, X. & Gao, H. (2012). Robust finite frequency H∞ filtering for uncertain 2-D Roesser systems. Automatica, 48, 1163-1170.
14. Li, X., Gao, H. & Wang, C. (2012). Generalized Kalman-Yakubovich- Popov Lemma for 2-D FM LSS model. IEEE Transactions on Automatic Control, 57, 3090-3103.
15. Lu, W. S. & Antoniou, A. (1992). Two-dimensional digital filters. New York: Marcel Dekker.
16. Palhares, R. M. & Peres, P. L. D. (1999). Robust H∞-filtering design with pole placement constraint via linear matrix inequalities. Journal of Optimization Theory and Applications, 102, 239-261.
17. Palhares, R. M. & Peres, P. L. D. (2000). Robust H∞ filter design with pole constraints for discrete-time systems. Journal of the Franklin Institute, 337, 713-723.
18. Paszke, W., Galkowski, K., Rogers, E. & Owens, D. H. (2006). H∞ and guaranteed cost control of discrete linear repetitive processes. Linear Algebra and Its Applications, 412, 93-131.
19. Paszke, W., Merry, R. & van de Molengraft, R. (2007). Iterative learning control by two-dimensional system theory applied to a motion system. In: Proc. American control conf., New York, USA (pp. 1833-1838).
20. Petersen, I. R. & Savkin, A. V. (1999). Robust Kalman filtering for signals and systems with large uncertainties. Boston: Birkhauser.
21. Sěbek, M. (1993). H∞ problem of 2-D systems. In: Proc. 1993 European control conf., Gröningen, Netherlands (pp. 1476-1479).
22. Shi, P., Boukas, E. K. & Agarwal, R. K. (1999). Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters. IEEE Transactions on Automatic Control, 44, 1592-1597.
23. Tuan, H. D., Apkarian, P. & Nguyen, T. Q. (2002). Robust mixed H2/H∞ filtering of 2-D systems. IEEE Transactions on Signal Processing, 50, 1759-1771.
24. Wang, Z., Liu, Y. & Liu, X. (2008). H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlineaities. Automatica, 44, 1268-1277.
25. Yang, R., Xie, L. & Zhang, C. (2008). Generalized two-dimensional Kalman-Yakubovich-Popov lemma for discrete Roesser model. IEEE Transactions on Circuits and Systems. I, Regular Papers, 55, 3223-3233.