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Non-fragile sampled data $$H_\infty$$ filtering of general continuous Markov jump linear. (English) Zbl 1309.93175
Summary: This paper is concerned with the non-fragile sampled data $$H_\infty$$ filtering problem for continuous Markov jump linear system with partly known transition probabilities (TPs). The filter gain is assumed to have additive variations and TPs are assumed to be known, uncertain with known bounds and completely unknown. The aim is to design a non-fragile $$H_\infty$$ filter to ensure both the robust stochastic stability and a prescribed level of $$H_\infty$$ performance for the filtering error dynamics. Sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities (LMIs). An example is provided to demonstrate the effectiveness of the proposed approach.

##### MSC:
 9.3e+13 Identification in stochastic control theory 9.3e+12 Filtering in stochastic control theory
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##### References:
 [1] Cao, Y., Frank, M.: Robust $$H_\infty$$ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Systems 8 (2000), 406-415. [2] Chang, X., Yang, G.: Nonfragile $$H_\infty$$ filtering of continuous-time fuzzy systems. IEEE Trans. Signal Process. 59 (2011), 1528-1538. · Zbl 1391.93134 [3] Chen, T., Francis, B.: Optimal Sampled-Data Control Systems. Springer, London 1995. · Zbl 0876.93002 [4] Gao, H., Sun, W., Shi, P.: Robust sampled-data control for vehicle active suspension systems. IEEE Trans. Control Systems Technol. 18 (2010), 238-245. [5] Hu, L., Shi, P., Huang, B.: Stochastic stability and robust control for sampled-data systems with Markovian jump parameters. J. Math. Anal. Appl. 313 (2006), 504-517. · Zbl 1211.93131 [6] Ji, Y., Chizeck, H. J.: Jump linear quadratic Gaussian control: Steady-state solution and testable conditions. Control Theory Advanced Technol. 6 (1990), 289-319. [7] Keel, L. H., Bhattacharyya, S. P.: Robust, fragile, or optimal?. IEEE Trans. Automat. Control 42 (1997), 1098-1105. · Zbl 0900.93075 [8] Lam, J., Shu, Z., Xu, S., Boukas, E. K.: Robust control of descriptor discrete-time Markovian jump systems. Int. J. Control 80 (2007), 374-385. · Zbl 1120.93057 [9] Mao, X.: Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl. 79 (1999), 45-67. · Zbl 0962.60043 [10] Shen, M., Yang, G.: $$H_2$$ filter design for discrete Markov jump linear system with partly unknown transition probabilities. Optimal Control Appl. Methods 33 (2012), 318-337. · Zbl 1276.93076 [11] Song, B., Xu, S., Zou, Y.: Non-fragile $$H_\infty$$ filtering for uncertain stochastic time-delay systems. Int. J. Innovative Comput. Inform. and Control 5 (2009), 2257-2266. [12] Sun, W., Nagpal, K. M., Khargonekar, P. P.: $$H_\infty$$ control and filtering for sampled-data systems. IEEE Trans. Automat. Control 38 (1993), 1162-1175. · Zbl 0784.93027 [13] Suplin, V., Fridman, E., Shaked, U.: Sampled-data $$H_\infty$$ control and filtering: Nonuniform uncertain sampling. Automatica 43 (2007), 1072-1083 · Zbl 1282.93171 [14] Xiong, J., Lam, J., Gao, H., Ho, D. W. C.: On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 41 (2005), 897-903. · Zbl 1093.93026 [15] Xu, S., Chen, T.: Robust $$H_\infty$$ filtering for uncertain impulsive stochastic systems under sampled measurements. Automatica 39 (2003), 509-516 · Zbl 1012.93063 [16] Xu, S., Chen, T.: Robust control for uncertain discrete-time stochastic bilinear systems with Markovian switching. Int. J. Robust Nonlinear 15 (2005), 201-217. · Zbl 1078.93025 [17] Yang, G., Che, W.: Non-fragile $$H_\infty$$ filter design for linear continuous-time systems. Automatica 44 (2008), 2849-2856. · Zbl 1152.93365 [18] Shi, P.: Filtering on sampled-data systems with parametric uncertainty. IEEE Trans. Automat. Control 43 (1998), 1022-1027. · Zbl 0951.93050 [19] Shi, P., Boukas, E. K., Agarwal, R. K.: Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters. IEEE Trans. Automat. Control 44 (1999), 1592-1597. · Zbl 0986.93066
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