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“Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems”

Authors: Bo Wang, Peng Shi, Hamid Reza Karimi and Xiucheng Dong,
Affiliation: Xihua University, University of Adelaide and University of Agder
Reference: 2012, Vol 33, No 4, pp. 131-139.

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Keywords: Stochastic stability; Markovian jump system, nonlinear system, time-varying delay

Abstract: In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system´s transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.

PDF PDF (329 Kb)        DOI: 10.4173/mic.2012.4.2

DOI forward links to this article:
  [1] Fangwen Li, Peng Shi, Xingcheng Wang and Hamid Reza Karimi (2014), doi:10.4173/mic.2014.3.3
  [2] Yuan-Qing Wu, Hongye Su, Renquan Lu, Zheng-Guang Wu and Zhan Shu (2015), doi:10.1016/j.sysconle.2015.08.001
  [3] Hamid Reza Karimi, Peng Shi and Bo Wang (2013), doi:10.1109/ASCC.2013.6606288
  [4] Peng Shi, Hamid Reza Karimi and Bo Wang (2013), doi:10.1109/ASCC.2013.6606289
  [5] Pengpeng Wang, Fei Long, Lu Guo and Yi Tan (2016), doi:10.1109/ChiCC.2016.7553863

[1] Bao, J., Houa, Z., Yuan, C. (2009). Stability in distribution of neutral stochastic differential delay equations with Markovian switching, Statistics and Probability Letters, 79:1663--1673 doi:10.1016/j.spl.2009.04.006
[2] Basin, M. Shi, P. (2009). Guest Editorial: New trends in optimal and robust filtering for stochastic systems, Circuits Systems and Signal Processing, 28:185--189 doi:10.1007/s00034-008-9076-1
[3] Boyd, S., Feron, L. G.E., Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory, Philadelphia, PA, SIAM.
[4] Cai, G., Hu, C., Duan, G. (2012). Efficient LMI-Based Quadratic Stability and Stabilization of Parameter-Dependent Interval Systems with Applications, International Journal of Innovative Computing, Information and Control, 8:1943--1954.
[5] Costa, O. Oliveira, A. (2012). Optimal mean - variance control for discrete-time linear systems with Markov jumps and multiplicative noises, Automatica, 48:304--315 doi:10.1016/j.automatica.2011.11.009
[6] Fei, Z., Gao, H., Shi, P. (2009). New results on stabilization of Markov jump systems with time delay, Automatica, 45:2300--2306 doi:10.1016/j.automatica.2009.06.020
[7] Gu, K. (2000). An integral inequality in the stability problem of time-delay systems, The 39th IEEE Conference on Decision Control, Sydney, Australia, pp. 2805--2810 doi:10.1109/CDC.2000.914233
[8] Karimi, H.R. (2011). Robust delay-dependent H-Infinity control of uncertain Markovian jump systems with mixed neutral, discrete and distributed time-delays, IEEE Trans. Circuits and Systems I, 58:1910--1923 doi:10.1109/TCSI.2011.2106090
[9] Karimi, H.R. (2012). A sliding mode approach to H-Infinity synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties, Journal of the Franklin Institute, 349:480--1496 doi:10.1016/j.jfranklin.2011.09.015
[10] Liu, J., Gu, Z., Hu, S. (2011). H-Infinity Filtering for Markovian Jump Systems with Time-Varying Delays, International Journal of Innovative Computing, Information and Control, 7:1299--1310.
[11] Liu, M., Shi, P., Zhang, L., Zhao, X. (2011). Fault tolerant control for nonlinear Markovian jump systems via proportional and derivative sliding mode observer, IEEE Trans on Circuits and Systems I: Regular Papers, 58:2755--2764 doi:10.1109/TCSI.2011.2157734
[12] Luan, X., Liu, F., Shi, P. (2010). Finite-time filtering for non-linear stochastic systems with partially known transition jump rates, IET Control Theory and Applications, 4:735--745 doi:0.1049/iet-cta.2009.0014
[13] Ma, H., Zhang, W., Hou, T. (2012). Infinite horizon H-2/H-Infinity control for discrete-time time-varying Markov jump systems with multiplicative noise, Automatica, 48:1447--1454 doi:10.1016/j.automatica.2012.05.006
[14] Shi, P. Liu, M. (2011). Discussion on 'On the filtering problem for continuous-time Markov jump linear systems with no observation of the Markov chain', European J. of Control, 17:355--356 doi:10.1007/s00034-008-9076-1
[15] Shi, P., Luan, X., Liu, F. (2012). H-Infinity filtering for discrete-time systems with stochastic incomplete measurement and mixed delays, IEEE Trans on Industrial Electronics, 59:2732--2739 doi:10.1109/TIE.2011.2167894
[16] Wang, G., Zhang, Q., Sreeram, V. (2010). Partially mode-dependent filtering for discrete-time Markovian jump systems with partly unknown transition probabilities, Signal Processing, 90:548--556 doi:10.1016/j.sigpro.2009.07.020
[17] Wu, L., Shi, P., Gao, H. (2010). State estimation and sliding mode control of Markovian jump singular systems, IEEE Trans on Automatic Control, 55:1213--1219 doi:10.1109/TAC.2010.2042234
[18] Wu, L., Su, X., Shi, P. (2012). Sliding mode control with bounded gain performance of Markov jump singular time-delay systems, Automatica, 48:1929--1933 doi:10.1016/j.automatica.2012.05.064
[19] Wu, Z., Shi, P., Su, H., Chu, J. (2011). L-2/L-Infinity filter design for discrete-time singular Markovian jump systems with time-varying delays, Information Sciences, 181:5534--5534 doi:10.1016/j.ins.2011.07.052
[20] Yin, Y., Shi, P., Liu, F., Pan, J. (2012). Gain-scheduled fault detection on stochastic nonlinear systems with partially known transition jump rates, Nonlinear Analysis: Real World Applications, 13:359--369 doi:10.1016/j.nonrwa.2011.07.043
[21] Zhang, L. (2009). H-Infinity estimation for discrete-time piecewise homogeneous Markov jump linear systems, Automatica, 45:2570--2576 doi:10.1016/j.automatica.2009.07.004
[22] Zhang, L., Boukas, K., Shi, P. (2009). H-Infinity model reduction for discrete-Time Markov Jump linear systems with partially known transition, Int. J. of Control, 82:243--351 doi:10.1080/00207170802098899
[23] Zhang, L., Boukas, K., Shi, P. (2011). Gain scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities, J. of Franklin Institute, 348:685--702 doi:10.1016/j.jfranklin.2011.01.011

  title={{Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems}},
  author={Wang, Bo and Shi, Peng and Karimi, Hamid Reza and Dong, Xiucheng},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


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