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Finite-time \(H_{\infty}\) control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching. (English) Zbl 1312.93109
Summary: An extension of a fixed Transition Probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time \(H_{\infty}\) control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov-Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.

MSC:
93E15 Stochastic stability in control theory
93B36 \(H^\infty\)-control
60J75 Jump processes (MSC2010)
93C55 Discrete-time control/observation systems
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References:
[1] DOI: 10.1109/TAC.2005.847042 · Zbl 1365.93182 · doi:10.1109/TAC.2005.847042
[2] DOI: 10.1016/j.automatica.2010.02.008 · Zbl 1191.93099 · doi:10.1016/j.automatica.2010.02.008
[3] DOI: 10.1016/S0005-1098(01)00087-5 · Zbl 0983.93060 · doi:10.1016/S0005-1098(01)00087-5
[4] DOI: 10.1137/S0363012997321358 · Zbl 0945.34039 · doi:10.1137/S0363012997321358
[5] DOI: 10.1016/j.jfranklin.2012.04.004 · Zbl 1300.93152 · doi:10.1016/j.jfranklin.2012.04.004
[6] DOI: 10.1002/oca.931 · Zbl 1213.93059 · doi:10.1002/oca.931
[7] Filardo A., Journal of Business and Economic Statistics 12 (3) pp 299– (1994)
[8] DOI: 10.1109/TAC.2010.2090575 · Zbl 1368.93679 · doi:10.1109/TAC.2010.2090575
[9] DOI: 10.1080/00207720903431785 · Zbl 1206.93113 · doi:10.1080/00207720903431785
[10] DOI: 10.1016/S0167-6911(02)00119-6 · Zbl 0994.93049 · doi:10.1016/S0167-6911(02)00119-6
[11] DOI: 10.1016/j.ins.2011.12.026 · Zbl 1248.93164 · doi:10.1016/j.ins.2011.12.026
[12] DOI: 10.1016/j.automatica.2004.11.036 · Zbl 1098.93032 · doi:10.1016/j.automatica.2004.11.036
[13] Krasovskii N., Automatic Remote Control 22 pp 1021– (1961)
[14] Lin X., Applied Mathematics and Computation 217 (12) pp 982– (2011)
[15] DOI: 10.1016/j.sigpro.2010.07.005 · Zbl 1203.94040 · doi:10.1016/j.sigpro.2010.07.005
[16] DOI: 10.1049/iet-cta.2009.0014 · doi:10.1049/iet-cta.2009.0014
[17] DOI: 10.1016/j.jfranklin.2009.09.006 · Zbl 1298.93290 · doi:10.1016/j.jfranklin.2009.09.006
[18] Qian C., IEEE Transactions on Automatic Control 50 (6) pp 549– (2005)
[19] DOI: 10.1080/00207721.2011.600472 · Zbl 1307.93445 · doi:10.1080/00207721.2011.600472
[20] DOI: 10.1016/j.automatica.2006.06.016 · Zbl 1113.60079 · doi:10.1016/j.automatica.2006.06.016
[21] DOI: 10.1016/j.japwor.2009.12.001 · doi:10.1016/j.japwor.2009.12.001
[22] DOI: 10.1016/j.jfranklin.2012.08.012 · Zbl 1264.93267 · doi:10.1016/j.jfranklin.2012.08.012
[23] DOI: 10.1016/j.neucom.2010.01.010 · Zbl 05721421 · doi:10.1016/j.neucom.2010.01.010
[24] DOI: 10.1016/j.cnsns.2011.09.022 · Zbl 1239.93036 · doi:10.1016/j.cnsns.2011.09.022
[25] DOI: 10.1007/s00034-012-9416-z · Zbl 1269.93125 · doi:10.1007/s00034-012-9416-z
[26] Yang Y., Journal of Systems Engineering and Electronics 21 (2) pp 2254– (2010)
[27] DOI: 10.1016/j.automatica.2009.07.004 · Zbl 1180.93100 · doi:10.1016/j.automatica.2009.07.004
[28] DOI: 10.1002/rnc.1355 · Zbl 1166.93320 · doi:10.1002/rnc.1355
[29] DOI: 10.1016/j.automatica.2009.02.002 · Zbl 1166.93378 · doi:10.1016/j.automatica.2009.02.002
[30] DOI: 10.1016/j.automatica.2008.08.010 · Zbl 1158.93414 · doi:10.1016/j.automatica.2008.08.010
[31] DOI: 10.1002/rnc.1276 · Zbl 1284.93238 · doi:10.1002/rnc.1276
[32] Zhang L., International Journal Innovative Computing, Information and Control 6 (2) pp 667– (2010)
[33] DOI: 10.1016/j.apm.2011.12.052 · Zbl 1252.93130 · doi:10.1016/j.apm.2011.12.052
[34] DOI: 10.1109/TFUZZ.2009.2013203 · doi:10.1109/TFUZZ.2009.2013203
[35] DOI: 10.1080/00207721.2012.760668 · Zbl 1317.93070 · doi:10.1080/00207721.2012.760668
[36] DOI: 10.1109/TNN.2010.2054108 · doi:10.1109/TNN.2010.2054108
[37] DOI: 10.1007/s00034-012-9420-3 · Zbl 1269.93131 · doi:10.1007/s00034-012-9420-3
[38] DOI: 10.1049/iet-cta.2011.0335 · doi:10.1049/iet-cta.2011.0335
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