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Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices. (English) Zbl 1209.93162
Summary: This paper focuses on stability and stabilization for a class of continuous-time Markovian jump systems with partial information on transition probability. The free-connection weighting matrix method is proposed to obtain a less conservative stability criterion of Markovian jump systems with partly unknown transition probability or completely unknown transition probability. As a result, a sufficient condition for a state feedback controller design is derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness and the merits of the proposed method.
MSC:
 93E15 Stochastic stability 60J75 Jump processes 15B48 Positive matrices and their generalizations; cones of matrices
References:
 [1] Boukas, E. K.: Stochastic switching systems: analysis and design, (2005) [2] Chen, W. H.; Guan, Z. H.; Lu, X. M.: Delay-dependent output feedback stabilisation of Markovian jump systems with time-delay, IEE Proceedings–control theory and applications 151, No. 5, 561-566 (2004) [3] Kushner, H. J.: Stochastic stability and control, (1967) [4] Li, H. Y.; Chen, B.; Zhou, Q.; Qian, W. Y.: Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters, IEEE transactions on systems, man and cybernetics, part B (Cybernetics) 39, No. 1, 94-102 (2009) [5] Lou, X. Y.; Cui, B. T.: Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays, IEEE transactions on systems, man and cybernetics, part B (Cybernetics) 37, No. 3, 713-719 (2007) [6] Mahmoud, M. S.: Delay-dependent H$\infty$ filtering of a class of switched discrete-time state delay systems, Signal processing 88, No. 11, 2709-2719 (2008) · Zbl 1151.93338 · doi:10.1016/j.sigpro.2008.05.014 [7] Mao, Z.; Jiang, B.; Shi, P.: H$\infty$ fault detection filter design for networked control systems modelled by discrete Markovian jump systems, IET control theory applications 1, No. 5, 1336-1343 (2007) [8] Martinelli, F.: Optimality of a two-threshold feedback control for a manufacturing system with a production dependent failure rate, IEEE transactions on automatic control 52, No. 10, 1937-1942 (2007) [9] Shi, P.; Mahmoud, M.; Nguang, S. K.; Ismail, A.: Robust filtering for jumping systems with mode-dependent delays, Signal processing 86, No. 1, 140-152 (2006) · Zbl 1163.94387 · doi:10.1016/j.sigpro.2005.05.005 [10] Shu, Z.; Lam, J.; Xu, S. Y.: Robust stabilization of Markovian delay systems with delay-dependent exponential estimates, Automatica 42, No. 11, 2001-2008 (2006) · Zbl 1113.60079 · doi:10.1016/j.automatica.2006.06.016 [11] Skorohod, A. V.: Asymptotic methods in the theory of stochastic differential equation, (1989) [12] Tao, F.; Zhao, Q.: Synthesis of active fault-tolerant control based on Markovian jump system models, IET control theory applications 1, No. 4, 1160-1168 (2007) [13] Wang, G. L.; Zhang, Q. L.; Sreeram, V.: Design of reduced-order H$\infty$ filtering for Markovian jump systems with mode-dependent time delays, Signal processing 89, No. 2, 187-196 (2009) · Zbl 1155.94337 · doi:10.1016/j.sigpro.2008.08.004 [14] Wu, Z.; Su, H.; Chu, J.: H$\infty$ model reduction for discrete singular Markovian jump systems, Proceedings of the institution of mechanical engineers, part I 223, No. 7, 1017-1025 (2009) [15] Xu, S. Y.; Mao, X. R.: Delay-dependent H$\infty$ control and filitering for uncertain Markovian jump system with time-varying delay, IEEE transactions on circuits and systems part I: Regular papers 54, No. 9, 2070-2077 (2007) [16] Zhang, L. X.; Boukas, E. K.: Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica 45, No. 2, 436-468 (2009) · Zbl 1158.93414 · doi:10.1016/j.automatica.2008.08.010 [17] Zhang, L. X.; Boukas, E. K.: Mode-dependent H$\infty$ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities, Automatica 45, No. 6, 1462-1467 (2009) · Zbl 1166.93378 · doi:10.1016/j.automatica.2009.02.002 [18] Zhang, L. X.; Boukas, E. K.: H$\infty$ control for discrete-time Markovian jump linear systems with partly unknown transition probabilities, International journal of robust and nonlinear control 19, No. 8, 868-883 (2009) · Zbl 1166.93320 · doi:10.1002/rnc.1355 [19] Zhang, L. X.; Boukas, E. K.; Lam, J.: Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities, IEEE transactions on automatic control 53, No. 10, 2458-2464 (2009) [20] Zhang, H. G.; Wang, Y. C.: Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays, IEEE transactions on neural networks 19, No. 2, 366-370 (2008)