Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information

Multidimensional Systems and Signal Processing

Volumn 26, Issue 3, 2015, Pages 575-597

  Wei, Yanling ^a   Qiu, Jianbin ^a   Karimi, Hamid Reza ^b   Wang, Mao ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF AGDER   (Norway)

Author keywords

Imperfect mode information; Markovian jump systems; Model approximation; State delays; Two dimensional systems

Indexed keywords

EID: 84934438129     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11045-013-0276-x     Document Type: Article

References (35)

1. Boukas, E. K. (2005). Stochastic switching systems: Analysis and design. Boston: Birkhauser.
2. de Souza, C. E. (2006). Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems. IEEE Transactions on Automatic Control, 51(5), 836–841.
3. El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 42(8), 1171–1176.
4. Gao, H., Lam, J., & Wang, C. (2006). Model simplification for switched hybrid systems. Systems & Control Letters, 55(12), 1015–1021.
5. Gao, H., Lam, J., Wang, C., & Wang, Q. (2004). Hankel norm approximation of linear systems with time-varying delay: Continuous and discrete cases. International Journal of Control, 77(17), 1503–1520.
6. Ghafoor, A., & Sreeram, V. (2008). Model reduction via limited frequency interval Gramians. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(9), 2806–2812.
7. Hoang, N. T., Tuan, H. D., Nguyen, T. Q., & Hosoe, S. (2005). Robust mixed generalized $${\mathscr {H}}_{2}/{\mathscr {H}}_{\infty }$$H2/H∞ filtering of 2-D nonlinear fractional transformation systems. IEEE Transactions on Signal Processing, 53(12), 4697–4706.
8. Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer.
9. Karan, M., Shi, P., & Kaya, C. Y. (2006). Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica, 42(12), 2159–2168.
10. Lam, J., Gao, H., Xu, S., & Wang, C. (2005). $$\mathscr {H}_{\infty }$$H∞ and $$\mathscr {L}_{2}$$L2-$$\mathscr {L}_{\infty }$$L∞ model reduction for system input with sector nonlinearities. Journal of Optimization Theory and Applications, 125(1), 137–155.
11. Lam, J., Xu, S., Zou, Y., Lin, Z., & Galkowski, K. (2004). Robust output feedback stabilization for two-dimensional continuous systems in Roesser form. Applied Mathematics Letters, 17(12), 1331–1341.
12. Lin, Z. (1999). Feedback stabilization of MIMO 3-D linear systems. IEEE Transactions on Automatic Control, 44(10), 1950–1955.
13. Lin, Z., Lam, J., Galkowski, K., & Xu, S. (2001). A constructive approach to stabilizability and stabilization of a class of nD systems. Multidimensional Systems and Signal Processing, 12(3–4), 329–343.
14. Liu, H., Ho, D. W. C., & Sun, F. (2008). Design of $$\mathscr {H}_{\infty }$$H∞ filter for Markov jumping linear systems with non-accessible mode information. Automatica, 44(10), 2655–2660.
15. Lu, W. S., & Antoniou, A. (1992). Two-dimensional digital filters. New York: Marcel Dekker.
16. Paszke, W., Lam, J., Galkowski, K., Xu, S., & Lin, Z. (2004). Robust stability and stabilisation of 2D discrete state-delayed systems. Systems & Control Letters, 51(3–4), 277–291.
17. Peng, D., & Guan, X. (2009). $${\mathscr {H}}_{\infty }$$H∞ filtering of 2-D discrete state delayed systems. Multidimensional Systems and Signal Processing, 20(3), 265–284.
18. Qiu, J., Feng, G., & Gao, H. (2012). Observer-based piecewise affine output feedback controller synthesis of continuous-time T-S fuzzy affine dynamic systems using quantized measurements. IEEE Transactions on Fuzzy Systems, 20(6), 1046–1062.
19. Roesser, R. P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1–10.
20. Wang, G., Zhang, Q., & Sreeram, V. (2009). Design of reduced-order $$\mathscr {H}_{\infty }$$H∞ filtering for Markovian jump systems with mode-dependent time delays. Signal Processing, 89(2), 187–196.
21. Wang, G., Zhang, Q., & Sreeram, V. (2010). Partially mode-dependent $$\mathscr {H}_{\infty }$$H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities. Signal Processing, 90(2), 548–556.
22. Wu, L., Shi, P., Gao, H., & Wang, C. (2006). $$\mathscr {H}_{\infty }$$H∞ mode reduction for two-dimensional discrete state-delayed systems. IEE Proceedings-Vision, Image and Signal Processing, 153(6), 769–784.
23. Wu, L., Shi, P., Gao, H., & Wang, C. (2008). $$\mathscr {H}_{\infty }$$H∞ filtering for 2-D Markovian jump systems. Automatica, 44(7), 1849–1858.
24. Wu, L., & Zheng, W. (2009). Weighted $$\mathscr {H}_{\infty }$$H∞ model reduction for linear switched systems with time-varying delay. Automatica, 45(1), 186–193.
25. Xie, L., Du, C., Soh, Y. C., & Zhang, C. (2002). $${\mathscr {H}}_{\infty }$$H∞ and robust control of 2-D systems in FM second model. Multidimensional Systems and Signal Processing, 13(3), 256–287.
26. Xu, H., Zou, Y., Xu, S., Lam, J., & Wang, Q. (2005). $$\mathscr {H}_{\infty }$$H∞ model reduction of 2-D singular Roesser models. Multidimensional Systems and Signal Processing, 16(3), 285–304.
27. Xu, S., Lam, J., Lin, Z., & Galkowski, K. (2002). Positive real control for uncertain two-dimensional systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 49(11), 1659–1666.
28. Xu, S., Lam, J., Lin, Z., Galkowski, K., Paszke, W., Sulikowski, B., et al. (2003). Positive real control of two-dimensional systems: Roesser models and linear repetitive processes. International Journal of Control, 76(11), 1047–1058.
29. Xu, S., Lam, J., & Mao, X. (2007). Delay-dependent $$\mathscr {H}_{\infty }$$H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems I: Regular Papers, 54(9), 2070–2077.
30. Xu, S., Lam, J., Zou, Y., Lin, Z., & Paszke, W. (2005). Robust $${\mathscr {H}}_{\infty }$$H∞ filtering for uncertain 2-D continuous systems. IEEE Transactions on Signal Processing, 53(5), 1731–1738.
31. Yan, W., & Lam, J. (1999). An approximation approach to $$\mathscr {H}_{2}$$H2 optimal model reduction. IEEE Transactions on Automatic Control, 44(7), 1341–1358.
32. Zhang, L., & Boukas, E. K. (2009). Mode-dependent $$\mathscr {H}_{\infty }$$H∞ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica, 45(6), 1462–1467.
33. Zhang, L., Huang, B., & Lam, J. (2003). $$\mathscr {H}_{\infty }$$H∞ model reduction of Markovian jump linear systems. Systems & Control Letters, 50(2), 103–118.
34. Zhao, Y., Zhang, L., Shen, S., & Gao, H. (2011). Robust stability criterion for discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions. IEEE Transactions on Neural Network, 22(1), 164–170.
35. Zhou, K. (1995). Frequency weighted $$\mathscr {L}_{\infty }$$L∞ norm and optimal Hankel norm model reduction. IEEE Transactions on Automatic Control, 40(10), 1687–1699.