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Neutral Passivity Filtering for Uncertain Markovian Jump Systems with Neutral-Retarded Mixed Time-Varying Delays

ZHAO Guowei, ZHUANG Guangming, XIA Jianwei, SUN Wei, CHEN Guoliang   

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng 252059
  • Received:2020-09-15 Revised:2021-06-14 Published:2022-03-16

ZHAO Guowei, ZHUANG Guangming, XIA Jianwei, SUN Wei, CHEN Guoliang. Neutral Passivity Filtering for Uncertain Markovian Jump Systems with Neutral-Retarded Mixed Time-Varying Delays[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(12): 3374-3394.

This paper deals with the problems of passivity analysis and passivity-based neutral-retarded mixed delays filter design for neutral Markovian jump systems (NMJSs) with time-varying delays and norm-bounded parametric uncertainties. Firstly, new delay-dependent conditions for the NMJSs are obtained by constructing a mode-dependent Lyapunov functional and introducing some free weight matrices (FWMs). Secondly, new mode-dependent neutral passivity filter is designed to ensure the passivity of the augmented neutral Markovian jump filtering error system via linear matrix inequalities (LMIs). A numerical example and a partial element equivalent circuit (PEEC) are utilized to show the effectiveness of the method.

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[1] Xu S, Lam J, Mao X. Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems I:Regular Papers, 2007, 54(9):2070-2077.
[2] Shu Z, Lam J, Xu S. Robust stabilization of Markovian delay systems with delay-dependent exponential estimates. Automatica, 2006, 42(11):2001-2008.
[3] 庄光明, 张化生, 赵军圣, 等. 中立随机马尔科夫跳变系统延迟反馈控制器设计. 聊城大学学报(自然科学版), 2018, 31(4):65-71. (Zhuang G, Zhang H S, Zhao J S, et al. Delay feedback controller design for neutral stochastic Markovian jump systems. Journal of Liaocheng University (Natural Science Edition), 2018, 31(4):65-71.)
[4] Zhang B, Zheng W X, Xu S. Delay-dependent passivity and passification for uncertain Markovian jump systems with time-varying delays. International Journal of Robust and Nonlinear Control, 2012, 22(16):1837-1852.
[5] 林玉倩, 尹月霞, 孙梦, 等. 时变时滞随机马尔科夫跳变系统非脆弱$H_{\infty }$动态输出反馈控制器设计. 聊城大学学报(自然科学版), 2021, 34(3):1-11, 17. (Lin Y Q, Yin Y X, Sun M, et al. Resilient H∞ dynamic output feedback controller design for stochastic jump systems with time-varying delays. Journal of Liaocheng University (Natural Science Edition), 2021, 34(3):1-11, 17.)
[6] Kavikumar R, Sakthivel R, Kwon O M, et al. Reliable non-fragile memory state feedback controller design for fuzzy Markov jump systems. Nonlinear Analysis:Hybrid Systems, DOI:10.1016/j.nahs.2019.100828.
[7] Zhang J, Li M, Raíssi T. Reliable actuator fault control of positive switched systems with double switchings. Asian Journal of Contral, 2020, DOI:10.1002/asjc.2338.
[8] Zhang J, Raíssi T. Saturation control of switched nonlinear systems. Nonlinear Analysis-Hybird Ststems, 2019, 32:43-44.
[9] Liu L, Zhang J, Shao Y, et al. Event-triggered control of positive switched systems based on linear programming. IET Contral Theory and Applications, 2019, 14(1):145-155.
[10] Song J, Niu Y, Lam J, et al. A hybrid design approach for output feedback exponential stabilization of Markovian jump systems. IEEE Transactions on Automatic Control, 2018, 63(5):1404-1417.
[11] Wu Z, Dong S, Su H, et al. Asynchronous dissipative control for fuzzy Markov jump systems. IEEE Transactions on Systems, Man, and Cybernetics, 2018, 48(8):2426-2436.
[12] Shen H, Li F, Xu S, et al. Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE Transactions on Automatic Control, 2017, 63(8):2709-2714.
[13] Zhuang G, Xia J, Feng J, et al. Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and Barbalat's lemma. IEEE Transactions on Systems, Man, and Cybernetics, DOI:10.1109/TSMC.2020.2964057.
[14] Feng Z, Shi P. Sliding mode control of singular stochastic Markov jump systems. IEEE Transactions on Automatic Control, 2017, 62(8):4266-4273.
[15] Li F, Xu S, Shen H. Fuzzy-model-based H∞ control for Markov jump nonlinear slow sampling singularly perturbed systems with partial information. IEEE Transactions on Fuzzy Systems, 2019, 27(10):1952-1962.
[16] Xiao X, Park J H, Zhou L, et al. New results on stability analysis of Markovian switching singular systems. IEEE Transactions on Automatic Control, 2019, 64(5):2084-2091.
[17] Zhao X, Yin Y, Niu B, et al. Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling. IEEE Transactions on Systems, Man, and Cybernetics, 2016, 46(8):1952-1957.
[18] Zhao X, Shi P, Yin Y, et al. New results on stability of slowly switched systems:A multiple discontinuous Lyapunov function approach. IEEE Transactions on Automatic Control, 2017, 62(7):3502-3509.
[19] Balasubramaniam P, Manivannan A, Rakkiyappan R. Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters. Applied Mathematics and Computation, 2010, 216(11):3396-3407.
[20] Shen H, Wang Y, Xia J W, et al. Fault-tolerant leader-following consensus for multi-agent systems subject to semi-Markov switching topologies:An event-triggered control scheme. Nonlinear Analysis:Hybrid Systems, 2019, 34:92-107.
[21] Wang Z, Shen L, Xia J, et al. Finite-time non-fragile l2-l control for jumping stochastic systems subject to input constraints via an event-triggered mechanism. Journal of the Franklin Institute, 2018, 355(14):6371-6389.
[22] Bemporad A, Bianchini G, Brogi F. Passivity analysis and passification of discrete-time hybrid systems. IEEE Transactions on Automatic Control, 2008, 53(4):1004-1009.
[23] Li C, Zhang H, Liao X. Passivity and passification of uncertain fuzzy systems. IEEE ProceedingsCircuits, Devices and Systems, 2005, 152(6):649-653.
[24] Gao H, Chen T, Chai T. Passivity and passification for networked control systems. SIAM Journal on Control and Optimization, 2007, 46(4):1299-1322.
[25] Yaesh I, Shaked U. Stochastic passivity and its application in adaptive control. Proceedings of the Joint 44th IEEE Conference on Decision and Control and 2005 European Control Conference, Seville, Spain, 2005, 2871-2876.
[26] Wei Y L, Qiu J B, Karimi H R. Quantized H∞ filtering for continuous-time Markovian jump systems with deficient mode information. Asian Journal of Contral, 2015, 17(5):1914-1923.
[27] Xue X J, Xu L, Xu H L. Distributed delay-dependent filtering for Markovian jump systems interconnected over an undirected graph with time-delay. Asian Journal of Contral, 2020, 22(3):1253-1267.
[28] Zhuang G, Su S F, Xia J, et al. HMM-based asynchronous H∞ filtering for fuzzy singular Markovian switching systems with retarded time-varying delays. IEEE Transactions on Cybernetics, 2020, 51(3):1189-1203.
[29] Wu Z, Dong S, Shi P, et al. Reliable filtering of nonlinear Markovian jump systems:The continuous-time case. IEEE Transactions on Systems Man And Cybernetics, 2019, 49(2):386-394.
[30] Shen Y, Wu Z, Shi P, et al. Asynchronous filtering for Markov jump neural networks with quantized outputs. IEEE Transactions on Systems, Man, and Cybernetics, 2019, 49(2):433-443.
[31] Wang Y, Zhuang G, Chen F. Event-based asynchronous dissipative filtering for T-S fuzzy singular Markovian jump systems with redundant channels. Nonlinear Analysis:Hybrid Systems, 2019, 34:264-283.
[32] Zhang B, Zheng W X, Xu S. Filtering of Markovian jump delay systems based on a new performance index. IEEE Transactions on Circuits and Systems I:Regular Papers, 2013, 60(5):1250-1263.
[33] Xiong J, Lam J. Fixed-order robust H∞ filter design for Markovian jump systems with uncertain switching probabilities. IEEE Transactions on Signal Processing, 2006, 54(4):1421-1430.
[34] Liu G, Xu S, Park J H, et al. Reliable exponential H∞ filtering for singular Markovian jump systems with time-varying delays and sensor failures. International Journal Robust Nonlinear Control, 2018, 28(14):4230-4245.
[35] Zhang D, Cheng J, Ahn C K, et al. A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay. Applied Mathematics and Computation, 2019, 342:191-205.
[36] Cheng J, Park J H, Karimi H R, et al. Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays. Information Sciences, 2017, 399:219-238.
[37] Xu S, Lam J. A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Sciences, 2008, 39(12):1095-1113.
[38] Zhuang G, Ma Q, Zhang B, et al. Admissibility and stabilization of stochastic singular Markovian jump systems with time-delays. Systems & Control Letters, 2018, 114:1-10.
[39] Wu L, Lam J. Sliding mode control of switched hybrid systems with time-varying delay. International Journal of Adaptive Control and Signal Processing, 2008, 22(10):909-931.
[40] Zhu S, Han Q L, Zhang C. L1-stochastic stability and L1-gain performance of positive Markov jump linear systems with time-delays:Necessary and sufficient conditions. IEEE Transactions on Automatic Control, 2017, 62(7):3634-3639.
[41] Zhuang G, Xia J, Zhang W, et al. State feedback control for stochastic Markovian jump delay systems based on LaSalle-type theorem. Journal of the Franklin Institute, 2018, 355(5):2179-2196.
[42] Yue D, Han Q. A Delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model. IEEE Transactions on Circults And Systems II:Express Briefs, 2004, 51(12):1321-1022.
[43] Xiong L, Tian J, Liu X. Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities. Journal of the Franklin Institute, 2012, 349:2193-2214.
[44] Zhang B, Xu S, Ma Q, et al. Output-feedback stabilization of singular LPV systems subject to inexact scheduling parameters. Automatica, 2019, 104:1-7.
[45] Chen Y, Qian W, Fei S. Improved robust stability conditions for uncertain neutral systems with discrete and distributed delays. Journal of the Franklin Institute, 2015, 352(7):2634-2645.
[46] Wu Z, Shi P, Shu Z, et al. Passivity-based asynchronous control for Markov jump systems. IEEE Transactions on Automatic Control, 2017, 62(4):2020-2025.
[47] Xia W, Li Y, Chu Y, et al. Observer-based mixed passive and H∞ control for uncertain Markovian jump systems with time delays using quantized measurements. Nonlinear Analysis:Hybrid Systems, 2019, 31:233-246.
[48] Mathiyalagan K, Park J H, Sakthivel R, et al. Robust mixed H∞ and passive filtering for networked Markov jump systems with impulses. Signal Processing, 2014, 101:162-173.
[49] Shen H, Wu Z G, Park J H. Reliable mixed passive and filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures. International Journal of Robust and Nonlinear Control, 2015, 25(17):3231-3251.
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