Asynchronous control of 2-D Markov jump systems subject to general probabilities information. (English) Zbl 1520.93540
Summary: This paper addresses the asynchronous control of 2-D Markov jump systems with general probabilities information based on the hidden Markov model, in which the partial information phenomena on transition probabilities and system mode are considered simultaneously. A hidden Markov model with general probabilities is utilized to describe partial information phenomena. By using the Lyapunov function approach, two \(H_\infty\) performance analysis criteria for the 2-D Markov jump systems with partial information on both transition probabilities and system mode are established, and the hidden Markov model-based controller design strategy is presented. The application of obtained theoretical results is illustrated via the Darboux equation with Markov jump parameters.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 93B36 | \(H^\infty\)-control |
| 62M05 | Markov processes: estimation; hidden Markov models |
Keywords:
asynchronous control; Markov jump systems; 2-D systems; hidden Markov model; general probabilities informationReferences:
| [1] | Kaczorek, T., Two-Dimensional Linear Systems (1985), Springer-Verlag: Springer-Verlag Berlin, Germany · Zbl 0593.93031 |
| [2] | Du, C.; Xie, L., \( H_\infty\) Control and Filtering of Two-Dimensional Systems (2002), Springer-Verlag: Springer-Verlag Berlin, Germany · Zbl 1013.93001 |
| [3] | Wu, L.; Wang, Z., Filtering and Control for Classes of Two-Dimensional Systems (2015), Springer: Springer London, U.K. · Zbl 1305.93004 |
| [4] | do Valle Costa, O. L.; Fragoso, M. D.; Marques, R. P., Discrete-Time Markov Jump Linear Systems (2005), Springer-Verlag: Springer-Verlag London, U.K. · Zbl 1081.93001 |
| [5] | Zhao, X.; Zeng, Q., New robust delay-dependent stability and \(H_\infty\) analysis for uncertain Markovian jump systems with time-varying delays, J. Franklin Inst., 347, 5, 863-874 (2010) · Zbl 1286.93199 |
| [6] | Chen, W.; Zhuang, G.; Xu, S.; Liu, G.; Li, Y.; Zhang, Z., New results on stabilization for neutral type descriptor hybrid systems with time-varying delays, Nonlinear Anal. Hybrid Syst., 45, Article 101172 pp. (2022) · Zbl 1497.93227 |
| [7] | 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, 10, 3082-3092 (2020) |
| [8] | Lian, J.; Wang, R., Stochastic stability of positive Markov jump linear systems with fixed dwell time, Nonlinear Anal. Hybrid Syst., 40, Article 101014 pp. (2021) · Zbl 1478.93714 |
| [9] | Hua, M.; Zheng, D.; Deng, F.; Fei, J.; Cheng, P.; Dai, X., \( H_\infty\) filtering for nonhomogeneous Markovian jump repeated scalar nonlinear systems with multiplicative noises and partially mode-dependent characterization, IEEE Trans. Syst. Man Cybern., 51, 5, 3180-3192 (2021) |
| [10] | Song, X.; Man, J.; Song, S.; Ahn, C. K., Finite/fixed-time anti-synchronization of inconsistent Markovian quaternion-valued memristive neural networks with reaction-diffusion terms, IEEE Trans. Circuits Syst. I. Regul. Pap., 68, 1, 363-375 (2021) |
| [11] | Kavikumar, R.; Sakthivel, R.; Liu, Y., Design of \(H_\infty \)-based sampled-data control for fuzzy Markov jump systems with stochastic sampling, Nonlinear Anal. Hybrid Syst., 41, Article 101041 pp. (2021) · Zbl 1478.93149 |
| [12] | Hua, M.; Qian, Y.; Deng, F.; Fei, J.; Cheng, P.; Chen, H., Filtering for discrete-time Takagi-Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects, Ieeec, 52, 2, 982-995 (2022) |
| [13] | 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, 9, Article 199204 pp. (2022) |
| [14] | Zhao, X.; Shi, P.; Yin, Y.; Nguang, S. K., New results on stability of slowly switched systems: A multiple discontinuous Lyapunov function approach, IEEE Trans. Automat. Control, 62, 7, 3502-3509 (2017) · Zbl 1370.34108 |
| [15] | Zhao, X.; Wang, X.; Ma, L.; Zong, G., Fuzzy approximation based asymptotic tracking control for a class of uncertain switched nonlinear systems, IEEE Trans. Fuzzy Syst., 28, 4, 632-644 (2020) |
| [16] | Wu, L.; Shi, P.; Gao, H.; Wang, C., \( H_\infty\) filtering for 2D Markovian jump systems, Automatica, 44, 7, 1849-1858 (2008) · Zbl 1149.93346 |
| [17] | Gao, H.; Lam, J.; Xu, S.; Wang, C., Stabilization and \(H_\infty\) control of two-dimensional Markovian jump systems, IMA J. Math. Control Inform., 21, 4, 377-392 (2004) · Zbl 1069.93007 |
| [18] | Zhang, L.; Boukas, E.-K.; Lam, J., Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities, IEEE Trans. Automat. Control, 53, 10, 2458-2464 (2008) · Zbl 1367.93710 |
| [19] | do Valle Costa, O. L.; Fragoso, M. D.; Todorov, M. G., A detector-based approach for the \(H_2\) control of Markov jump linear systems with partial information, IEEE Trans. Automat. Control, 60, 5, 1219-1234 (2015) · Zbl 1360.93761 |
| [20] | Hien, L. V.; Trinh, H., Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities, Inform. Sci., 367, 403-417 (2016) · Zbl 1429.93404 |
| [21] | Ghous, I.; Xiang, Z.; Karimi, H. R., \( H_\infty\) control of 2-D continuous Markovian jump delayed systems with partially unknown transition probabilities, Inform. Sci., 382, 274-291 (2017) · Zbl 1432.93085 |
| [22] | Wei, Y.; Qiu, J.; Karimi, H. R.; Wang, M., Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information, Inform. Sci., 269, 316-331 (2014) · Zbl 1339.93111 |
| [23] | Wu, L.; Yao, X.; Zheng, W. X., Generalized \(H_2\) fault detection for two-dimensional Markovian jump systems, Automatica, 48, 8, 1741-1750 (2012) · Zbl 1268.93096 |
| [24] | Wang, Y.; Xia, J.; Shen, H.; Cao, J., HMM-based quantized dissipative control for 2-D Markov jump systems, Nonlinear Anal. Hybrid Syst., 40, Article 101018 pp. (2021) · Zbl 1478.93674 |
| [25] | Wu, Z.-G.; Shen, Y.; Shi, P.; Shu, Z.; Su, H., \( H_\infty\) control for 2-D Markov jump systems in Roesser model, IEEE Trans. Automat. Control, 64, 1, 427-432 (2019) · Zbl 1423.93408 |
| [26] | Hien, L. V.; Trinh, H., Observer-based control of 2-D Markov jump systems, IEEE Trans. Circuits Syst. II Express Briefs, 64, 11, 1322-1326 (2017) |
| [27] | Cheng, P.; Wang, H.; Stojanovic, V.; He, S.; Shi, K.; Luan, X.; Liu, F.; Sun, C., Asynchronous fault detection observer for 2-D Markov jump systems, IEEE Trans. Cybern., 52, 12, 13623-13634 (2022) |
| [28] | Wu, Z.-G.; Tao, Y.-Y., Asynchronous guaranteed cost control of 2-D Markov jump Roesser systems, IEEE Trans. Cybern., 52, 12, 13063-13072 (2022) |
| [29] | 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, 8, 3701-3706 (2020) · Zbl 1533.93758 |
| [30] | Shen, Y.; Wu, Z.-G.; Shi, P.; Wen, G., Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes, Automatica, 106, 8-17 (2019) · Zbl 1429.93388 |
| [31] | Gonçalves, A. P.; Fioravanti, A. R.; Geromel, J. C., Filtering of discrete-time Markov jump linear systems with uncertain transition probabilities, Internat. J. Robust Nonlinear Control, 21, 6, 613-624 (2011) · Zbl 1213.93190 |
| [32] | Luan, X.; Zhao, S.; Liu, F., \( H_\infty\) control for discrete-time Markov jump systems with uncertain transition probabilities, IEEE Trans. Automat. Control, 58, 6, 1566-1572 (2012) · Zbl 1369.93178 |
| [33] | Li, X.; Lam, J.; Gao, H.; Xiong, J., \( H_\infty\) and \(H_2\) filtering for linear systems with uncertain Markov transitions, Automatica, 67, 252-266 (2016) · Zbl 1335.93126 |
| [34] | Shen, Y.; Wu, Z.-G.; Shi, P.; Wen, G., Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes, Automatica, 106, 8-17 (2019) · Zbl 1429.93388 |
| [35] | Li, F.; Xu, S.; Shen, H.; Zhang, Z., Extended dissipativity-based control for hidden Markov jump singularly perturbed systems subject to general probabilities, IEEE Trans. Syst. Man Cybern., 51, 9, 5752-5761 (2021) |
| [36] | Song, J.; Niu, Y.; Zou, Y., Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities, Automatica, 93, 33-41 (2018) · Zbl 1400.93052 |
| [37] | Zhu, J.; Li, C.; Dullerud, G. E., Asynchronous \(H_\infty\) control for two-dimensional hidden Markovian jump systems with partly known mode observation conditional probabilities, Internat. J. Robust Nonlinear Control, 30, 8, 3344-3364 (2020) · Zbl 1466.93043 |
| [38] | Wang, Y.; Zhuang, G.; Chen, X.; Wang, Z.; Chen, F., Dynamic event-based finite-time mixed \(H_\infty\) and passive asynchronous filtering for T-S fuzzy singular Markov jump systems with general transition rates, Nonlinear Anal. Hybrid Syst., 36, Article 100874 pp. (2020) · Zbl 1441.93071 |
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