Song, Xiaona; Man, Jingtao; Song, Shuai; Wang, Zhen Finite-time nonfragile time-varying proportional retarded synchronization for Markovian inertial memristive NNs with reaction-diffusion items. (English) Zbl 1443.93120 Neural Netw. 123, 317-330 (2020). Summary: The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction-diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported. Cited in 10 Documents MSC: 93D40 Finite-time stability 93E15 Stochastic stability in control theory 93C20 Control/observation systems governed by partial differential equations 93B70 Networked control Keywords:inertial memristive neural networks; reaction-diffusion items; Markovian jump parameters; nonfragile time-varying proportional retarded control; finite-time interval PDFBibTeX XMLCite \textit{X. Song} et al., Neural Netw. 123, 317--330 (2020; Zbl 1443.93120) Full Text: DOI References: [1] Ahn, S.; Rubchinsky, L. L., Short desynchronization episodes prevail in synchronous dynamics of human brain rhythms, Chaos, 23, 1, 1926 (2013) [2] Chen, C.; Li, L.; Peng, H.; Yang, Y., Fixed-time synchronization of inertial memristor-based neural networks with discrete delay, Neural Networks, 109, 81-89 (2019) · Zbl 1441.93278 [3] Cheng, J.; Park, J. H.; Cao, J.; Qi, W., Hidden markov model-based nonfragile state estimation of switched neural network with probabilistic quantized outputs, IEEE Transactions on Cybernetics (2019) [4] Chua, L., Memristor-the missing circuit element, IEEE Transactions on Circuit Theory, 18, 5, 507-519 (1971) [5] Dharani, S.; Rakkiyappan, R.; Park, J. H., Pinning sampled-data synchronization of coupled inertial neural networks with reaction-diffusion terms and time-varying delays, Neurocomputing, 227, 101-107 (2017) [6] Ding, Z.; Shen, Y., Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling, IEEE Transactions on Cybernetics, 44, 8, 1350-1361 (2014) [7] Ding, S.; Wang, Z.; Wang, J.; Zhang, H., \( H_\infty\) State estimation for memristive neural networks with time-varying delays: the discrete-time case, Neural Networks, 84, 47-56 (2016) · Zbl 1429.93365 [8] Fan, Y.; Huang, X.; Shen, H.; Cao, J., Switching event-triggered control for global stabilization of delayed memristive neural networks: an exponential attenuation scheme, Neural Networks, 117, 216-224 (2019) · Zbl 1443.93079 [9] Guo, Z.; Gong, S.; Huang, T., Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control, Neurocomputing, 293, 100-107 (2018) [10] He, S.; Liu, F., Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters, Neurocomputing, 103, 1, 87-92 (2013) [11] Huang, D.; Jiang, M.; Jian, J., Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control, Neurocomputing, 266, 527-539 (2017) [12] Kao, Y.; Wang, C.; Karimi, H. R.; Ran, B., Global stability of coupled Markovian switching reaction-diffusion systems on networks, Journal of Systems Science & Complexity, 13, 5, 61-73 (2014) · Zbl 1292.93140 [13] Karimi, H. R., A sliding mode approach to \(H_\infty\) synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties, Journal of the Franklin Institute, 349, 4, 1480-1496 (2012) · Zbl 1254.93046 [14] Karimi, H. R.; Gao, H., New delay-dependent exponential \(H_\infty\) synchronization for uncertain neural networks with mixed time delays, IEEE Transactions on Systems Man & Cybernetics, 40, 1, 173-185 (2010) [15] Li, X.; Li, X.; Hu, C., Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method, Neural Networks, 96, 91 (2017) · Zbl 1441.93227 [16] Li, R.; Wei, H., Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms via sampled data control, International Journal of Machine Learning & Cybernetics, 7, 1, 157-169 (2016) [17] Liu, Y.; Arunkumar, A.; Sakthivel, R.; Nithya, V.; Alsaadi, F., Finite-time event-triggered non-fragile control and fault detection for switched networked systems with random packet losses, Journal of the Franklin Institute (2019) · Zbl 1450.93059 [18] Liu, Y.; Park, J. H.; Guo, B.; Shu, Y., Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control, IEEE Transactions on Fuzzy Systems, 26, 4, 1040-1045 (2018) [19] Lu, J., Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, Chaos, Solitons & Fractals, 35, 1, 116-125 (2008) · Zbl 1134.35066 [20] Ma, Q.; Feng, G.; Xu, S., Delay-dependent stability criteria for reaction-diffusion neural networks with time-varying delays, IEEE Transactions on Cybernetics, 43, 6, 1913-1920 (2013) [21] Mathiyalagan, K.; Anbuvithya, R.; Sakthivel, R.; Park, J. H.; Prakash, P., Non-fragile \(H_\infty\) synchronization of memristor-based neural networks using passivity theory, Neural Networks, 74, 85-100 (2016) · Zbl 1398.34109 [22] Park, P. G.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076 [23] Park, J. H.; Shen, H.; Chang, X.; Lee, T. H., Recent advances in control and filtering of dynamic systems with constrained signals (2019), Springer: Springer Cham, Switzerland · Zbl 1429.93004 [24] Rakkiyappan, R.; Premalatha, S.; Chandrasekar, A.; Cao, J., Stability and synchronization analysis of inertial memristive neural networks with time delays, Cognitive Neurodynamics, 10, 5, 437-451 (2016) [25] Saravanakumar, R.; Rajchakit, G.; Ahn, C. K.; Karimi, H. R., Exponential stability, passivity, and dissipativity analysis of generalized neural networks with mixed time-varying delays, IEEE Transactions on Systems Man & Cybernetics Systems, 49, 2, 395-405 (2019) [26] Senan, S.; Syed, A. M.; Vadivel, R.; Arik, S., Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays, Neural Networks, 86, 32-41 (2017) · Zbl 1429.93010 [27] Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 9, 2860-2866 (2013) · Zbl 1364.93740 [28] Shen, H.; Wang, T.; Cao, J.; Lu, J.; Song, Y.; Huang, T., Nonfragile dissipative synchronization for Markovian memristive neural networks: a gain-scheduled control scheme, IEEE Transactions on Neural Networks & Learning Systems (2018) [29] Shen, H.; Zhu, Y.; Zhang, L.; Park, J. H., Extended dissipative state estimation for Markov jump neural networks with unreliable links, IEEE Transactions on Neural Networks & Learning Systems, 28, 2, 346-358 (2016) [30] Song, X.; Wang, M.; Song, S.; Wang, Z., Intermittent pinning synchronization of reaction-diffusion neural networks with multiple spatial diffusion couplings, Neural Computing and Applications (2019) [31] Song, X.; Wang, M.; Song, S.; Wang, Z., Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links, Applied Mathematics and Computation, 353, 371-395 (2019) · Zbl 1428.93073 [32] Tao, J.; Wu, Z.; Su, H.; Wu, Y.; Zhang, D., Asynchronous and resilient filtering for Markovian jump neural networks subject to extended dissipativity, IEEE Transactions on Cybernetics (2018) [33] Tu, Z.; Cao, J.; Alsaedi, A.; Alsaadi, F., Global dissipativity of memristor-based neutral type inertial neural networks, Neural Networks, 88, 125-133 (2017) · Zbl 1461.94106 [34] Tu, Z.; Cao, J.; Hayat, T., Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks, Neural Networks, 75, 47-55 (2016) · Zbl 1415.92025 [35] Wan, P.; Jian, J., Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays, ISA Transactions, 74, 88-98 (2018) [36] Wang, Y.; Yang, W.; Xiao, J.; Zeng, Z., Impulsive multisynchronization of coupled multistable neural networks with time-varying delay, IEEE Transactions on Neural Networks & Learning Systems, 28, 7, 1560-1571 (2017) [37] Wang, L.; Zeng, Z.; Ge, M.; Hu, J., Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays, Neural Networks, 105, 65-74 (2018) · Zbl 1441.93255 [38] Wei, R.; Cao, J., Fixed-time synchronization of quaternion-valued memristive neural networks with time delays, Neural Networks, 113, 1-10 (2019) · Zbl 1441.93285 [39] Wen, S.; Zeng, Z.; Huang, T.; Yu, X., Noise cancellation of memristive neural networks, Neural Networks, 60, 74-83 (2014) · Zbl 1323.93052 [40] Wen, S.; Zeng, Z.; Huang, T.; Zhang, Y., Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators, IEEE Transactions on Fuzzy Systems, 22, 6, 1704-1713 (2014) [41] Wu, Z.; Shi, P.; Shu, Z.; Su, H.; Lu, R., Passivity-based asynchronous control for Markov jump systems, IEEE Transactions on Automatic Control, 62, 4, 2020-2025 (2017) · Zbl 1366.93611 [42] Xiao, Q.; Huang, T.; Zeng, Z., Passivity and passification of fuzzy memristive inertial neural networks on time scales, IEEE Transactions on Fuzzy Systems (2018) [43] Yang, X.; Feng, Z.; Feng, J.; Cao, J., Synchronization of discrete-time neural networks with delays and markov jump topologies based on tracker information, Neural Networks, 85, 157-164 (2017) · Zbl 1429.93346 [44] Yang, S.; Guo, Z.; Wang, J., Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling, IEEE Transactions on Systems Man & Cybernetics Systems, 45, 7, 1077-1086 (2015) [45] Zhang, G.; Hu, J.; Zeng, Z., New criteria on global stabilization of delayed memristive neural networks with inertial item, IEEE Transactions on Cybernetics (2019) [46] Zhang, Z.; Quan, Z., Global exponential stability via inequality technique for inertial BAM neural networks with time delays, Neurocomputing, 151, 1316-1326 (2015) [47] Zhang, H.; Sheng, Y.; Zeng, Z., Synchronization of coupled reaction-diffusion neural networks with directed topology via an adaptive approach, IEEE Transactions on Neural Networks & Learning Systems, 29, 5, 1550-1561 (2018) [48] Zhang, W.; Yang, S.; Li, C.; Zhang, W.; Yang, X., Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control, Neural Networks, 104, 93-103 (2018) · Zbl 1441.93334 [49] Zhang, G.; Zeng, Z.; Hu, J., New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays, Neural Networks, 97, 183-191 (2018) · Zbl 1442.34121 [50] Zhang, R.; Zeng, D.; Park, J. H.; Liu, Y.; Zhong, S., A new approach to stabilization of chaotic systems with nonfragile fuzzy proportional retarded sampled-data control, IEEE Transactions on Cybernetics (2018) 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.