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Robust control of uncertain discrete-time Markovian jump systems with actuator saturation. (English) Zbl 1330.93238

Summary: The robust stochastic stabilization problem for the class of discrete-time uncertain Markovian jump linear systems (MJLS) with actuator saturation is considered. The definition of domain of attraction in mean square sense (DoA-MSS) is introduced to analyze the stochastic stability of the closed-loop system. By using a class of stochastic Lyapunov function which is dependent on the jump mode and saturation function, design procedures for both the mode-dependent and mode-independent state feedback controllers are developed based on the Linear Matrix Inequality (LMI) approach. Finally, a numerical example is provided to show the usefulness of the proposed techniques.

MSC:

93E15 Stochastic stability in control theory
93B35 Sensitivity (robustness)
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[1] DOI: 10.1080/00207170500267929 · Zbl 1081.93016
[2] DOI: 10.1002/(SICI)1099-1239(1998110)8:13<1155::AID-RNC380>3.0.CO;2-F · Zbl 0918.93060
[3] DOI: 10.1109/9.989152 · Zbl 1364.93843
[4] Boukas EK, Deterministic and Stochastic Time Delay Systems (2002)
[5] DOI: 10.1023/A:1025443220763 · Zbl 1045.93039
[6] Boukas EK, Stochastic Switching Systems: Analysis and Design (2005)
[7] DOI: 10.1016/S0167-6911(02)00128-7 · Zbl 0994.93014
[8] Cao YY, Automatica 39 pp 1235– (2003)
[9] DOI: 10.1016/S0005-1098(98)00202-7 · Zbl 0933.93079
[10] Daraoui, N, Benzaouia, A and Boukas, EK. 2003. Regulator problem for linear discrete-time delay systems with Markovian jumping parameters and constrained control. Proc. of 42nd IEEE Int. Conf. on Decision and Control. 2003. pp.2806–2810. Vol. 3,
[11] DOI: 10.1109/TAC.2003.817012 · Zbl 1364.93210
[12] DOI: 10.1109/TSP.2004.827188 · Zbl 1369.93175
[13] DOI: 10.1002/(SICI)1099-1239(199611)6:9/10<1015::AID-RNC266>3.0.CO;2-0 · Zbl 0863.93067
[14] DOI: 10.1016/S0167-6911(01)00168-2 · Zbl 0987.93027
[15] DOI: 10.1007/978-1-4612-0205-9
[16] DOI: 10.1109/9.57016 · Zbl 0714.93060
[17] DOI: 10.1016/j.automatica.2004.10.011 · Zbl 1061.93045
[18] Mohammed, B and Khalid, B. 2003. A design of constrained controllers for linear systems with Markovian jumps. Proc. of Int. Conf. on Machine Learning Models Technologies and Applications. 2003. pp.256–260. 256
[19] DOI: 10.1016/j.automatica.2004.11.034 · Zbl 1087.49022
[20] DOI: 10.1016/S0167-6911(99)00035-3 · Zbl 0948.93058
[21] DOI: 10.1109/9.802932 · Zbl 1078.93575
[22] DOI: 10.1080/00207170310001638605 · Zbl 1050.93063
[23] de Souza CE, Proc. of IEEE Int. Conf. on Decision and Control pp 2811– (2003)
[24] de Souza CE, Control Theory and Advanced Technology 9 pp 457– (1993)
[25] DOI: 10.1109/9.995042 · Zbl 1364.93672
[26] DOI: 10.1109/TSP.2004.826180 · Zbl 1370.93291
[27] DOI: 10.1016/j.automatica.2004.12.001 · Zbl 1093.93026
[28] DOI: 10.1109/TAC.2003.820138 · Zbl 1364.93229
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