Delay-dependent synchronization of T-S fuzzy Markovian jump complex dynamical networks. (English) Zbl 1467.93013
Summary: In this paper, a delay-dependent synchronization criteria for Markovian jump complex dynamical networks subject to time-varying coupling delays and external disturbances are proposed via Takagi-Sugeno (T-S) fuzzy approach. The class of Markovian jump complex dynamical networks is described by a fuzzy model composed of two levels such as a crisp level which represents the jumps and a fuzzy level which describes the system nonlinearities. An asymptotic synchronization criterion is obtained by employing fuzzy controller with the mixed \(H_\infty\) and passivity performance index \(\nu > 0\). Further, by constructing a novel Lyapunov-Krasovskii functional along with the extended integral inequality and using the properties of Kronecker product and convex combination approach, a set of sufficient constraints is derived in the form of linear matrix inequalities and checked for its feasibility using MATLAB software. At last, numerical simulations including the Lorentz system are given to demonstrate the applicability and effectiveness of the developed results.
MSC:
| 93A14 | Decentralized systems |
| 93C42 | Fuzzy control/observation systems |
| 93E03 | Stochastic systems in control theory (general) |
| 93D50 | Consensus |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
Keywords:
complex dynamical networks; asymptotic synchronization; T-S fuzzy model; Markovian jump parametersSoftware:
MatlabReferences:
| [1] | Selvaraj, P.; Sakthivel, R.; Ahn, C. K., Observer-based synchronization of complex dynamical networks under actuator saturation and probabilistic faults, IEEE Trans. Syst. Man Cybern. Syst., 49, 7, 1516-1526 (2018) |
| [2] | Selvaraj, P.; Sakthivel, R.; Kwon, O. M., Synchronization of fractional-order complex dynamical network with random coupling delay, actuator faults and saturation, Nonlinear Dyn., 94, 4, 3101-3116 (2018) · Zbl 1422.34162 |
| [3] | Chen, X.; Park Ju, H.; Cao, J.; Qiu, J., Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control, Neurocomputing, 273, 9-21 (2018) |
| [4] | Wang, Y.; Song, D.; Gao, X.; Qu, S. X.; Lai, Y. C.; Wang, X., Effect of network structural perturbations on spiral wave patterns, Nonlinear Dyn., 93, 3, 1671-1680 (2018) |
| [5] | Radenkovic, M. S.; Krstic, M., Distributed adaptive consensus and synchronization in complex networks of dynamical systems, Automatica, 91, 233-243 (2018) · Zbl 1387.93022 |
| [6] | Liu, Y.; Guo, B. Z.; Park Ju, H.; Lee, S. M., Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control, IEEE Trans. Neural Netw. Learn. Syst., 29, 1, 118-128 (2018) |
| [7] | Wang, Z.; Wang, Y.; Liu, Y., Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays, IEEE Trans. Neural Netw., 21, 1, 11-25 (2010) |
| [8] | Li, Z.; Chen, G., Global synchronization and asymptotic stability of complex dynamical networks, IEEE Trans. Circuits Syst. II, Express Briefs, 53, 1, 28-33 (2006) |
| [9] | Zhang, Q.; Lu, J.; Lu, J.; Chi, K. T., Adaptive feedback synchronization of a general complex dynamical network with delayed nodes, IEEE Trans. Circuits Syst. II, Express Briefs, 55, 2, 183-187 (2018) |
| [10] | Su, H.; Rong, Z.; Chen, M. Z.Q.; Wang, X.; Chen, G.; Wang, H., Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks, IEEE Trans. Cybern., 43, 1, 394-399 (2013) |
| [11] | Liu, G.; Luo, Y.; Shu, L., Asymptotic synchronization of complex dynamical networks with time-varying delays on time scales, Eng. Lett., 26, 2, 210-215 (2018) |
| [12] | Li, Q.; Guo, J.; Wu, Y.; Sun, C. Y., Global asymptotical bounded synchronization for a class of coupled complex networks with nonidentical nodes, Asian J. Control, 19, 4, 1630-1640 (2017) · Zbl 1370.93039 |
| [13] | Park, M. J.; Kwon, O. M.; Park Ju, H.; Lee, S. M.; Cha, E. J., Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays, Appl. Math. Comput., 218, 23, 11634-11647 (2012) · Zbl 1277.93047 |
| [14] | Chang, W. J.; Ku, C. C.; Huang, P. H., Robust fuzzy control for uncertain stochastic time-delay Takagi-Sugeno fuzzy models for achieving passivity, Fuzzy Sets Syst., 161, 15, 2012-2032 (2010) · Zbl 1194.93114 |
| [15] | Li, X. J.; Yang, G. H., Fuzzy approximation-based global pinning synchronization control of uncertain complex dynamical networks, IEEE Trans. Cybern., 47, 4, 873-883 (2017) |
| [16] | Wang, Y.; Yu, H., Fuzzy synchronization of chaotic systems via intermittent control, Chaos Solitons Fractals, 106, 154-160 (2018) · Zbl 1392.93029 |
| [17] | Mahdavi, N.; Menhaj, M. B.; Kurths, J.; Lu, J., Fuzzy complex dynamical networks and its synchronization, IEEE Trans. Cybern., 43, 2, 648-659 (2013) |
| [18] | Yang, X.; Yang, Z., Synchronization of T-S fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects, Fuzzy Sets Syst., 235, 25-43 (2014) · Zbl 1315.93055 |
| [19] | Wu, Y.; Lu, R.; Shi, P.; Su, H.; Wu, Z. G., Sampled-data synchronization of complex networks with partial couplings and T-S fuzzy nodes, IEEE Trans. Fuzzy Syst., 26, 2, 782-793 (2018) |
| [20] | Wen, T.; Jiang, W., Identifying influential nodes based on fuzzy local dimension in complex networks, Chaos Solitons Fractals, 119, 332-342 (2019) · Zbl 1448.05167 |
| [21] | Yang, S.; Li, C.; Huang, T.; Zhang, W., Fixed-time consensus of complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties, Fuzzy Sets Syst., 365, 81-97 (2019) · Zbl 1423.93223 |
| [22] | Zhang, Y.; Yang, Y.; Shi, P.; Pan, J. S., Finite-time boundedness of Markovain jump nonlinear systems with incomplete information, Int. J. Syst. Sci., 49, 16, 3296-3306 (2018) · Zbl 1482.93553 |
| [23] | Ye, Z.; Ji, H.; Zhang, H., Passivity analysis of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations, Chaos Solitons Fractals, 83, 147-157 (2016) · Zbl 1355.60101 |
| [24] | Peng, H.; Lu, R.; Xu, Y.; Yao, F., Dissipative non-fragile state estimation for Markovian complex networks with coupling transmission delays, Neurocomputing, 275, 1576-1584 (2018) |
| [25] | Ren, H.; Deng, F.; Peng, Y., Finite time synchronization of Markovian jumping stochastic complex dynamical systems with mix delays via hybrid control strategy, Neurocomputing, 272, 683-693 (2018) |
| [26] | Wang, P.; Hong, Y.; Su, H., Stabilization of stochastic complex-valued coupled delayed systems with Markovian switching via periodically intermittent control, Nonlinear Anal. Hybrid Syst., 29, 395-413 (2018) · Zbl 1388.93101 |
| [27] | Su, L.; Ye, D., Mixed \(H_\infty\) and passive event-triggered reliable control for T-S fuzzy Markov jump systems, Neurocomputing, 281, 96-105 (2018) |
| [28] | Wang, J.; Su, L.; Shen, H.; Wu, Z. G.; Park Ju, H., Mixed \(H_\infty \)/passive sampled-data synchronization control of complex dynamical networks with distributed coupling delay, J. Franklin Inst., 354, 3, 1302-1320 (2017) · Zbl 1355.93113 |
| [29] | Park Ju, H.; Shen, H.; Chang, X. H.; Lee, T. H., Mixed \(H_\infty \)/passive synchronization for complex dynamical networks with sampled-data control, (Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals, vol. 170 (2019)), 211-223 · Zbl 1429.93004 |
| [30] | Liu, Y.; Wang, Z.; Ma, L.; Cui, Y.; Alsaadi, F. E., Synchronization of directed switched complex networks with stochastic link perturbations and mixed time-delays, Nonlinear Anal. Hybrid Syst., 27, 213-224 (2018) · Zbl 1378.93117 |
| [31] | Wang, J. L.; Wu, H. N.; Huang, T., Passivity-based synchronization of a class of complex dynamical networks with time-varying delay, Automatica, 56, 105-112 (2015) · Zbl 1323.93012 |
| [32] | Wang, X.; Liu, X.; She, K.; Zhong, S.; Shi, L., Delay-dependent impulsive distributed synchronization of stochastic complex dynamical networks with time-varying delays, IEEE Trans. Syst. Man Cybern. Syst., 49, 7, 1496-1504 (2018) |
| [33] | Seuret, A.; Liu, K.; Gouaisbaut, F., Generalized reciprocally convex combination lemmas and its application to time-delay systems, Automatica, 95, 488-493 (2018) · Zbl 1402.93193 |
| [34] | Tang, Z.; Park Ju, H.; Feng, J., Novel approaches to pin cluster synchronization on complex dynamical networks in Lur’e forms, Commun. Nonlinear Sci. Numer. Simul., 57, 422-438 (2018) · Zbl 1510.93294 |
| [35] | Sathishkumar, M.; Sakthivel, R.; Kwon, O. M.; Kaviarasan, B., Finite-time mixed \(H_\infty\) and passive filtering for Takagi-Sugeno fuzzy nonhomogeneous Markovian jump systems, Int. J. Syst. Sci., 48, 7, 1416-1427 (2017) · Zbl 1362.93090 |
| [36] | Sakthivel, R.; Sakthivel, R.; Selvaraj, P.; Karimi, H. R., Delay-dependent fault-tolerant controller for time-delay systems with randomly occurring uncertainties, Int. J. Robust Nonlinear Control, 27, 18, 5044-5060 (2017) · Zbl 1381.93039 |
| [37] | Gong, D.; Zhang, H.; Wang, Z.; Liu, J., Synchronization analysis for complex networks with coupling delay based on T-S fuzzy theory, Appl. Math. Model., 36, 12, 6215-6224 (2012) · Zbl 1349.93246 |
| [38] | Xu, D.; Gui, W.; Zhao, P.; Yang, C., Hybrid synchronization of general T-S fuzzy complex dynamical networks with time-varying delay, Math. Probl. Eng., Article 384654 pp. (2013) · Zbl 1296.93100 |
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.
