Non-fragile \(H_\infty\) filtering for delayed discrete-time Markov jump systems: an adaptive event-triggered strategy. (English) Zbl 1539.93185
Summary: This paper deals with the problem of non-fragile filter for delayed discrete-time Markov jump systems. The purpose is to design a mode-dependent filter such that the result filtering error system is stochastically stable and satisfies a prescribed \(H_\infty\) performance lever \(\gamma\). In order to improve the data transmission efficient, an adaptive event-triggered strategy is introduced. Then, with the help of the Lyapunov stability theory and matrix inequality, the sufficient conditions for the solution of the filter design problem proposed are established. Finally, two numerical examples are presented to verification the effectiveness of the proposed method.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93E15 | Stochastic stability in control theory |
| 93C43 | Delay control/observation systems |
| 93C40 | Adaptive control/observation systems |
| 93C65 | Discrete event control/observation systems |
References:
| [1] | Moon, J., Linear-quadratic stochastic leader-follower differential games for Markov jump-diffusion models, Automatica, 147, Article 110713 pp., 2023 · Zbl 1505.91056 |
| [2] | Balenzuela, M. P.; Wills, A. G.; Renton, C.; Ninness, B., A new smoothing algorithm for jump Markov linear systems, Automatica, 140, Article 110218 pp., 2022 · Zbl 1485.93557 |
| [3] | Bueno, J. N.A. D.; Marcos, L. B.; Rocha, K. D.T.; Terra, M. H., Regulation of Markov jump linear systems subject to polytopic uncertainties, IEEE Trans. Automat. Control, 67, 6279-6286, 2022 · Zbl 1541.93069 |
| [4] | Vargas, A. N.; Agulhari, C. M.; Oliveira, R. C.L. F.; Preciado, V. M., Robust stability analysis of linear parameter-varying systems with Markov jumps, IEEE Trans. Automat. Control, 67, 6234-6239, 2022 · Zbl 1541.93261 |
| [5] | Shen, H.; Zhang, Y.; Wang, J.; Cao, J.; Rutkowski, L., Observer-based control for discrete-time hidden semi-Markov jump systems, IEEE Trans. Automat. Control, 68, 6255-6261, 2023 · Zbl 07794469 |
| [6] | Wang, J.; Xia, J.; Shen, H.; Xing, M.; Park, J. H., \( H_\infty\) Synchronization for fuzzy Markov jump chaotic systems with piecewise-constant transition probabilities subject to PDT switching rule, IEEE Trans. Fuzzy Syst., 29, 3082-3092, 2022 |
| [7] | Shen, H.; Xing, M.; Yan, H.; Cao, J., Observer-based \(l_2- l_\infty\) control for singularly perturbed semi-Markov jump systems with improved weighted TOD protocol, Sci. China Inf. Sci., 65, Article 199204 pp., 2022 |
| [8] | Li, F.; Xu, S.; Shen, H.; Ma, Q., Passivity-based control for hidden Markov jump systems with singular perturbations and partially unknown probabilities, IEEE Trans. Automat. Control, 65, 3701-3706, 2020 · Zbl 1533.93758 |
| [9] | da Silva, L. P.M.; Goncalves, A. P.C., \( H_2\) and \(H_\infty\) filtering for continuous-time Markov jump Lur’e systems with sector bound optimization, Internat. J. Control, 96, 1336-1351, 2023 · Zbl 1519.93220 |
| [10] | Xia, W.; Zheng, W. X.; Xu, S., Realizability condition for digital filters with time delay using generalized overflow arithmetic, IEEE Trans. Circuits Syst. II, Exp. Briefs, 66, 1, 141-145, 2019 |
| [11] | Xia, W.; Li, Y.; Li, Z.; Jia, X.; Chen, W.; Chen, H., Event-triggered filtering for uncertain semi-Markov jump systems with time-varying delay by using quantized measurement, J. Franklin Inst., 359, 7091-7114, 2022 · Zbl 1496.93081 |
| [12] | Chen, W.; Gao, F.; She, J.; Xia, W., Further results on delay-dependent stability for neutral singular systems via state decomposition method, Chaos Solitons Fractals, 141, Article 110408 pp., 2020 · Zbl 1496.34109 |
| [13] | Shen, Y.; Wu, Z.; Shi, P.; Huang, T., Asynchronous filtering for Markov jump neural networks with quantized outputs, IEEE Trans. Syst., 49, 433-443, 2019 |
| [14] | Yin, Y.; Zhuang, G.; Xia, J.; Chen, G., Asynchronous \(H_\infty\) filtering for singular Markov jump neural networks with mode-dependent time-varying delays, Neural Process. Lett., 54, 5439-5456, 2022 |
| [15] | Yin, Y.; Zhuang, G.; Xia, J.; Ma, Q.; Sun, W., \( H_\infty\) Asynchronous deconvolution fuzzy filter design for nonlinear singular Markov jump systems with time-varying delays, Int. J. Fuzzy Syst., 25, 763-779, 2023 |
| [16] | Lehmann, F.; Pieczynski, W., Suboptimal Kalman filtering in triplet Markov models using model order reduction, IEEE Signal Process. Lett., 27, 1100-1104, 2023 |
| [17] | Lehmann, F.; Pieczynski, W., Reduced-dimension filtering in triplet Markov models, IEEE Trans. Automat. Control, 67, 605-617, 2022 · Zbl 1537.93748 |
| [18] | Tao, J.; Xiao, Z.; Rao, H.; Wu, J.; Lu, R.; Shi, P.; Wang, X., Event-triggered and asynchronous reduced-order filtering codesign for fuzzy Markov jump systems, IEEE Trans. Syst., 52, 3937-3946, 2021 |
| [19] | de Oliveira, A. M.; Costa, O. L.V.; Barros dos Santos, S. R.; Gabriel, G. W., Reduced-order energy-to-peak filtering for hidden Markov jump linear systems, J. Franklin Inst., 360, 251-276, 2023 · Zbl 1506.93094 |
| [20] | Zhang, L.; Sun, Y.; Li, H.; Liang, H.; Wang, J., Event-triggered fault detection for nonlinear semi-Markov jump systems based on double asynchronous filtering approach, Automatica, 138, Article 110144 pp., 2022 · Zbl 1485.93370 |
| [21] | Zhang, K.; Braverman, E., Event-triggered impulsive control for nonlinear systems with actuation delays, IEEE Trans. Automat. Control, 68, 540-547, 2023 · Zbl 1541.93227 |
| [22] | Yu, H.; Hao, F.; Chen, T., A uniform analysis on input-to-state stability of decentralized event-triggered control systems, IEEE Trans. Automat. Control, 64, 3423-3430, 2019 · Zbl 1482.93533 |
| [23] | G. Cui, H. Xu, J. Yu, H.K. Lam, Event-triggered distributed fixed-time adaptive attitude control with prescribed performance for multiple QUAVs, IEEE Trans. Autom. Sci. Eng., http://dx.doi.org/10.1109/TASE.2023.3297235. |
| [24] | Cui, G.; Xu, H.; Chen, X.; Yu, J., Fixed-time distributed adaptive formation control for multiple QUAVs with full-state constraints, IEEE Trans. Aerosp. Electron. Syst., 59, 4192-4206, 2023 |
| [25] | Shen, H.; Liu, Y.; Shi, K.; Park, J. H.; Wang, J., Event-based distributed secondary control for AC islanded microgrid with semi-Markov switched topology under cyber-attacks, IEEE Syst. J., 17, 2927-2938, 2023 |
| [26] | Xu, Z.; Ding, B.; Zhang, T., Event-based state and fault estimation for stochastic nonlinear system with Markov packet dropout, J. Franklin Inst., 359, 1649-1666, 2022 · Zbl 1481.93129 |
| [27] | Li, C.; Ran, G.; Liu, J.; Sakthivel, R.; Gao, Y., Event-based asynchronous output feedback control for nonlinear Markov jump systems with partially unknown transition probabilities, IEEE Trans. Circuits Syst., 69, 3525-3529, 2022 |
| [28] | Xiao, Z.; Chen, J.; Xu, M.; Zhang, X.; Tao, J., Asynchronous output feedback control for Markov jump systems under dynamic event-triggered strategy, Internat. J. Robust Nonlinear Control, 32, 10087-10100, 2022 · Zbl 1529.93036 |
| [29] | Liang, R.; Xiao, Z.; Wu, Z.; Tao, J.; Wang, X., Dynamic event-triggered and asynchronous sliding mode control for T-S fuzzy Markov jump systems, Nonlinear Dynam., 109, 911-924, 2022 |
| [30] | Shen, H.; Liu, Y.; Wang, J.; Yan, H.; Chadli, M., Sliding-mode control for IT2 fuzzy nonlinear singularly perturbed systems and its application to electric circuits: a dynamic event-triggered mechanism, IEEE Trans. Syst. Man Cybern. Syst., 53, 4077-4090, 2023 |
| [31] | Tao, J.; Xiao, Z.; Li, Z.; Wu, J.; Lu, R.; Shi, P.; Wang, X., Dynamic event-triggered state estimation for Markov jump neural networks with partially unknown probabilities, IEEE Trans. Neural Netw. Learn. Syst., 33, 7438-7447, 2022 |
| [32] | Zhang, X.; Wang, H.; Song, J.; He, S.; Sun, C., Co-design of adaptive event generator and asynchronous fault detection filter for Markov jump systems via genetic algorithm, IEEE Trans. Cybern., 53, 5059-5068, 2023 |
| [33] | Ran, G.; Liu, J.; Li, C.; Lam, H.; Li, D.; Chen, H., Fuzzy-model-based asynchronous fault detection for Markov jump systems with partially unknown transition probabilities: an adaptive event-triggered approach, IEEE Trans. Fuzzy Syst., 30, 4679-4689, 2022 |
| [34] | Yin, K.; Yang, D., Asynchronous fault detection filter of positive Markov jump systems by dynamic event-triggered mechanism, ISA Trans., 138, 197-211, 2023 |
| [35] | Zhang, Z.; Zhang, H.; Wang, Z.; Shan, Q., Non-fragile exponential \(H_\infty\) control for a class of nonlinear networked control systems with short time-varying delay via output feedback controller, IEEE Trans. Cybern., 47, 2008-2019, 2017 |
| [36] | Shu, Z.; Lam, J.; Xiong, J., Non-fragile exponential stability assignment of discrete-time linear systems with missing data in actuators, IEEE Trans. Automat. Control, 54, 625-630, 2009 · Zbl 1367.93481 |
| [37] | Shen, H.; Hu, X.; Wang, J.; Cao, J.; Qian, W., Non-fragile \(H_\infty\) synchronization for Markov jump singularly perturbed coupled neural networks subject to double-layer switching regulation, IEEE Trans. Neural Netw. Learn. Syst., 34, 2682-2692, 2023 |
| [38] | Li, F.; Xu, S.; Zhang, B., Resilient asynchronous \(H_\infty\) control for discrete-time Markov jump singularly perturbed systems based on hidden Markov model, IEEE Trans. Syst. Man, Cybern. Cybern, 50, 2860-2869, 2020 |
| [39] | Tao, J.; Wu, Z.; Su, H.; Wu, Y.; Zhang, D., Asynchronous and resilient filtering for Markovian jump neural networks subject to extended dissipativity, IEEE Trans. Cybern., 49, 2504-2513, 2019 |
| [40] | Shen, M.; Park. S. Fei, J. H., Event-triggered nonfragile \(H_\infty\) filtering of Markov jump systems with imperfect transmissions, Signal Process., 149, 204-213, 2018 |
| [41] | Deng, X.; Zhang, J.; Raissi, T., Event-triggered positive \(l_1\)-gain non-fragile filter design for positive Markov jump systems, Inform. Sci., 573, 562-584, 2021 · Zbl 1530.93263 |
| [42] | Zhang, L.; Boukas, E. K., Mode-dependent \(H_\infty\) filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities, Automatica, 45, 1462-1467, 2009 · Zbl 1166.93378 |
| [43] | Xia, W.; Li, Y.; Chu, Y.; Xu, S.; Chen, W.; Zhang, Z., Observer-based mixed passive and \(H_\infty\) control for uncertain Markovian jump systems with time delays using quantized measurements, Nonlinear Anal. Hybrid Syst., 31, 233-246, 2019 · Zbl 1408.93059 |
| [44] | Seuret, A.; Gouaisbaut, F.; Fridman, E., Stability of discrete-time systems with time-varying delays via a novel summation inequality, IEEE Trans. Autom. Control., 60, 2740-2745, 2015 · Zbl 1360.93612 |
| [45] | Park, P. G.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 235-238, 2011 · Zbl 1209.93076 |
| [46] | Cao, Y.; Lam, J., Robust \(H_\infty\) control of uncertain Markovian jump systems with time-delay, IEEE Trans. Autom. Control., 45, 77-83, 2000 · Zbl 0983.93075 |
| [47] | Wang, G.; Xie, R.; Zhang, H.; Yu, G.; Dang, C., Robust exponential \(H_\infty\) filtering for discrete-time switched fuzzy systems with time-varying delay, Circuits Syst. Signal Process., 35, 117-138, 2016 · Zbl 1346.93382 |
| [48] | Shi, S.; Fei, Z.; Shi, P.; Ahn, C. K., Asynchronous filtering for discrete-time switched T-S fuzzy systems, IEEE Trans. Fuzzy Syst., 28, 1531-1541, 2020 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
