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$\cal H_{\infty}$ filtering for 2D Markovian jump systems. (English) Zbl 1149.93346
Summary: This paper is concerned with the problem of $\cal H_{\infty}$ filtering for 2D discrete Markovian jump systems. The mathematical model of 2D jump systems is established upon the well-known Roesser model. Our attention is focused on the design of a full-order filter, which guarantees the filtering error system to be mean-square asymptotically stable and has a prescribed $\cal H_{\infty}$ disturbance attenuation performance. Sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities, and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software. A numerical example is provided to illustrate the effectiveness of the proposed design method.

93E11Filtering in stochastic control
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
93E03General theory of stochastic systems
Full Text: DOI
[1] Aberkane, S.; Ponsart, J. Christophe; Sauter, D.: Output feedback H$\infty $control of a class of stochastic hybrid systems with Wiener process via convex analysis, International journal of innovative computing, information and control 6, 1179-1196 (2006)
[2] Apkarian, P.; Tuan, H. D.; Bernussou, J.: Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations, IEEE transactions on automatic control 46, 1941-1946 (2001) · Zbl 1003.93016 · doi:10.1109/9.975496
[3] Basin, M.; Perez, J.; Martinez-Zuniga, R.: Optimal filtering for nonlinear polynomial systems over linear observations with delay, International journal of innovative computing, information and control 2, 863-874 (2006)
[4] Boukas, E. K.; Yang, H.: Exponential stabilizability of stochastic systems with Markovian jumping parameters, Automatica 35, 1437-1441 (1999) · Zbl 0932.93084 · doi:10.1016/S0005-1098(99)00033-3
[5] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory, (1994) · Zbl 0816.93004
[6] Cao, Y. Y.; Lam, J.: Robust H$\infty $control of uncertain Markovian jump systems with time delay, IEEE transactions on automatic control 45, 77-83 (2000) · Zbl 0983.93075 · doi:10.1109/9.827358
[7] Du, C.; Xie, L.; Zhang, C.: H$\infty $control and robust stabilization of two-dimensional systems in roesser models, Automatica 37, 205-211 (2001) · Zbl 0970.93013 · doi:10.1016/S0005-1098(00)00155-2
[8] Gao, H.; Lam, J.; Wang, C.; Xu, S.: Robust H$\infty $filter for uncertain 2D stochastic systems, Circuits systems and signal processing 23, 479-505 (2004) · Zbl 1175.93222
[9] Gao, H.; Lam, J.; Xu, S.; Wang, C.: Stabilization and H$\infty $control of two-dimensional Markovian jump systems, IMA journal of mathematical and control information 21, 377-392 (2004) · Zbl 1069.93007 · doi:10.1093/imamci/21.4.377
[10] Hinamoto, T.: Stability of 2-D discrete systems described by the fornasini-marchesini second model, IEEE transactions on circuits and systems (I) 44, 254-257 (1997)
[11] Hoang, N. T.; Tuan, H. D.; Nguyen, T. Q.; Hosoe, S.: Robust mixed generalized H2/H$\infty $filtering of 2-D nonlinear fractional transformation systems, IEEE transactions on signal processing 53, 4697-4706 (2005)
[12] Ji, Y.; Chizeck, H. J.: Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control, IEEE transactions on automatic control 35, 777-788 (1990) · Zbl 0714.93060 · doi:10.1109/9.57016
[13] Lu, W. S.: On a Lyapunov approach to stability analysis of 2-D digital filters, IEEE transactions on circuits and systems (I) 41, 665-669 (1994)
[14] Lu, W. S.; Antoniou, A.: Two-dimensional digital filters, (1992) · Zbl 0852.93001
[15] Marszalek, W.: Two-dimensional state-space discrete models for hyperbolic partial differential equations, Applied mathematical and modeling 8, 11-14 (1984) · Zbl 0529.65039 · doi:10.1016/0307-904X(84)90170-7
[16] Shi, P.; Boukas, E. K.; Agarwal, R. K.: Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE transactions on automatic control 44, 1592-1597 (1999) · Zbl 0986.93066 · doi:10.1109/9.780431
[17] Tuan, H. D.; Apkarian, P.; Nguyen, T. Q.: Robust mixed H2/H$\infty $filtering of 2-D systems, IEEE transactions on signal processing 50, 1759-1771 (2002)
[18] Wang, Z.; Lam, J.; Liu, X. H.: Robust filtering for discrete-time Markovian jump delay systems, IEEE transactions on signal processing letters 11, 659-662 (2004)
[19] Wu, L.; Shi, P.; Gao, H.; Wang, C.: H$\infty $mode reduction for two-dimensional discrete state-delayed systems, IEE Proceedings part J: vision, image and signal processing 153, 769-784 (2006)
[20] Wu, L.; Wang, Z.; Gao, H.; Wang, C.: H$\infty $and l2-l$\infty $filtering for two-dimensional linear parametervarying systems, International journal of robust & nonlinear control 17, 1129-1154 (2007) · Zbl 1266.93153
[21] Wu, L.; Wang, Z.; Gao, H.; Wang, C.: Robust H$\infty $filtering for uncertain two-dimensional discrete systems with state delays, Signal processing 87, 2213-2230 (2007) · Zbl 1186.94370 · doi:10.1016/j.sigpro.2007.03.002
[22] Xie, L.; Ogai, H.; Inoe, Y.: Numerical solving of hybrid dynamic switching system and its application, International journal of innovative computing, information and control 2, 849-862 (2006)
[23] Xiong, J.; Lam, J.; Gao, H.; Ho, D. W. C.: On robust stabilization of Markovian jump systems with uncertain switching probabilities, Automatica 41, 897-903 (2005) · Zbl 1093.93026 · doi:10.1016/j.automatica.2004.12.001
[24] Xu, S.; Chen, T.; Lam, J.: Robust H$\infty $filtering for uncertain Markovian jump systems with mode-dependent time-delays, IEEE transactions on automatic control 48, 900-907 (2003)
[25] Xu, S.; Chen, T.; Lam, J.: Robust H$\infty $filtering for a class of nonlinear discrete-time Markovian jump systems, Journal of optimization theory and applications 122, 651-668 (2004) · Zbl 1082.93056 · doi:10.1023/B:JOTA.0000042599.46775.a9
[26] Yue, D.; Fang, J.; Won, S.: Delay-dependent robust stability of stochastic uncertain systems with time delay and Markovian jump parameters, Circuits, systems and signal processing 22, 351-365 (2003) · Zbl 1048.93095 · doi:10.1007/s00034-004-7036-y
[27] Zhang, H.; Basin, M.; Skliar, M.: Optimal state estimation for continuous, stochastic, state-space system with hybrid measurements, International journal of innovative computing, information and control 2, 357-370 (2006)
[28] Zhang, L.; Huang, B.; Lam, J.: H$\infty $model reduction of Markovian jump linear systems, Systems & control letters 50, 103-118 (2003) · Zbl 1157.93519 · doi:10.1016/S0167-6911(03)00133-6