Synchronization of complex networks with time-varying delay of unknown bound via delayed impulsive control. (English) Zbl 1447.93153
Summary: The synchronization problem for complex networks with time-varying delays of unknown bound is investigated in this paper. From the impulsive control point of view, a novel delayed impulsive differential inequality is proposed, where the bounds of time-varying delays in continuous dynamic and discrete dynamic are both unknown. Based on the inequality, a class of delayed impulsive controllers is designed to achieve the synchronization of complex networks, where the restriction between impulses interval and time-varying delays is dropped. A numerical example is presented to illustrate the effectiveness of the obtained results.
MSC:
| 93C27 | Impulsive control/observation systems |
| 93C43 | Delay control/observation systems |
| 93B70 | Networked control |
Keywords:
time-varying delay; delayed impulsive control; complex networks; synchronization; impulsive differential inequalityReferences:
| [1] | Ali, S.; Usha, M.; Orman, Z.; Arik, S., Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control, Neural Networks, 114, 28-37 (2019) · Zbl 1441.93306 |
| [2] | Chen, W.; Jiang, Z.; Lu, X.; Luo, S., \( H_\infty\) Synchronization for complex dynamical networks with coupling delays using distributed impulsive control, Nonlinear Analysis. Hybrid Systems, 17, 111-127 (2015) · Zbl 1351.34091 |
| [3] | Chen, T.; Wang, L., Global \(\mu \)-stability of delayed neural networks with unbounded time-varying delays, IEEE Transactions on Neural Networks, 18, 1836-1840 (2007) |
| [4] | Cui, H.; Guo, J.; Feng, J.; Wang, T., Global \(\mu \)-stability of impulsive reaction-diffusion neural networks with unbounded time-varying delays and bounded continuously distributed delays, Neurocomputing, 157, 1-10 (2015) |
| [5] | Faydasicok, O.; Arik, S., Further analysis of global robust stability of neural networks with multiple time delays, Journal of the Franklin Institute, 349, 813-825 (2012) · Zbl 1273.93124 |
| [6] | Faydasicok, O.; Arik, S., A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks, Neural Networks, 44, 64-71 (2013) · Zbl 1296.92085 |
| [7] | Faydasicok, O.; Arik, S., A new robust stability criterion for dynamical neural networks with multiple time delays, Neurocomputing, 99, 290-297 (2013) |
| [8] | Guan, Z.; Zhang, H., Stabilization of complex network with hybrid impulsive and switching control, Chaos, Solitons & Fractals, 37, 1372-1382 (2008) · Zbl 1142.93423 |
| [9] | He, W.; Qian, F.; Cao, J., Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Networks, 85, 1-9 (2017) · Zbl 1429.93351 |
| [10] | Hu, B.; Song, Q.; Li, K.; Zhao, Z.; Liu, Y.; Alsaadi, F., Global \(\mu \)-synchronization of impulsive complex-valued neural networks with leakage delay and mixed time-varying delays, Neurocomputing, 307, 106-116 (2018) |
| [11] | Khadra, A.; Liu, X.; Shen, X., Impulsively synchronizingchaotic systems with delay and applications to secure communication, Automatica, 41, 1491-1502 (2005) · Zbl 1086.93051 |
| [12] | Lee, S.; Park, M.; Kwon, M.; Sakthivel, R., Advanced sampled-data synchronization control for complex dynamical networks with coupling time-varying delays, Information Sciences, 420, 454-465 (2017) · Zbl 1447.93209 |
| [13] | Li, H.; Cao, J.; Hu, C.; Zhang, L.; Wang, Z., Global synchronization between two fractional-order complex networks with non-delayed and delayed coupling via hybrid impulsive control, Neurocomputing, 356, 31-39 (2019) |
| [14] | Li, X.; Martin, B., An impulsive delay differential inequality and applications, Computers and Mathematics with Applications, 64, 1875-1881 (2012) · Zbl 1268.34159 |
| [15] | Li, X.; Song, S.; Wu, J., Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Transactions on Automatic Control, 64, 4024-4034 (2019) · Zbl 1482.93452 |
| [16] | Lin, D.; Li, X.; O’Regan, D., \( \mu \)-stability of infinite delay functional differential systems with impulsive effects, Applicable Analysis, 92, 15-26 (2013) · Zbl 1266.34122 |
| [17] | Liu, X.; Zhang, K., Synchronization of linear dynamical networks on time scales: pinning control via delayed impulses, Automatica, 72, 147-152 (2016) · Zbl 1344.93071 |
| [18] | Lv, X.; Rakkiyappan, R.; Li, X., \( \mu \)-stability criteria for nonlinear differential systems with additive leakage and transmission time-varying delays, Nonlinear Analysis: Modeling and Control, 23, 380-400 (2018) · Zbl 1420.34093 |
| [19] | Naghshtabrizi, P.; Hespanha, J.; Teel, A., Exponential stability of impulsive systems with application to uncertain sampled-data systems, Systems & Control Letters, 57, 378-385 (2008) · Zbl 1140.93036 |
| [20] | Ozcan, N.; Ali, M.; Yogambigai, J.; Zhu, Q.; Arik, S., Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction-diffusion terms via sampled-data control, Journal of the Franklin Institute, 355, 1192-1216 (2018) · Zbl 1393.93080 |
| [21] | 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) |
| [22] | Selvaraj, P.; Kwon, M.; Sakthivel, R., Disturbance and uncertainty rejection performance for fractional-order complex dynamical networks, Neural Networks, 112, 73-84 (2019) · Zbl 1447.93263 |
| [23] | Tan, X.; Cao, J., Intermittent control with double event-driven for leader-following synchronization in complex networks, Applied Mathematical Modelling, 64, 372-385 (2018) · Zbl 1480.93012 |
| [24] | Tang, R.; Yang, X.; Wan, X., Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers, Neural Networks, 113, 79-90 (2019) · Zbl 1441.93264 |
| [25] | Wang, L.; Chen, T., Multiple \(\mu \)-stability of neural networks with unbounded time-varying delays, Neural Networks, 53, 109-118 (2014) · Zbl 1307.93365 |
| [26] | Wang, Z.; Liu, X., Exponential stability of impulsive complex-valued neural networks with time delay, Mathematics and Computers in Simulation, 156, 143-157 (2019) · Zbl 1540.34141 |
| [27] | Wang, X.; Liu, X.; She, K.; Zhong, S., Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes, Nonlinear Analysis. Hybrid Systems, 26, 307-318 (2017) · Zbl 1379.34049 |
| [28] | Wang, Y.; Lu, J.; Lou, Y., Halanay-type inequality with delayed impulses and its applications, Science China. Information Sciences, 62, 192206 (2019) |
| [29] | Wang, L.; Song, Q., Pricing policies for dual-channel supply chain with green investment and sales effort under uncertain demand, Mathematics and Computers in Simulation (2019) |
| [30] | Yang, X.; Li, X.; Xi, Q.; Duan, P., Review of stability and stabilization for impulsive delayed systems, Mathematical Bioscience and Engineering, 15, 1495-1515 (2018) · Zbl 1416.93159 |
| [31] | Yang, Z.; Xu, D., Stability analysis of delay neural networks with impulsive effects, IEEE Transactions on Circuits and Systems-II: Express Briefs, 52, 517-521 (2005) |
| [32] | Yu, R.; Zhang, H.; Wang, Z.; Liu, Y., Synchronization criterion of complex networks with time-delay under mixed topologies, Neurocomputing, 295, 8-16 (2018) |
| [33] | Zhang, J.; Sun, J., Exponential synchronization of complex networks with continuous dynamics and Boolean mechanism, Neurocomputing, 307, 146-152 (2008) |
| [34] | Zhang, L.; Yang, X.; Xu, C.; Feng, J., Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control, Applied Mathematics and Computation, 306, 22-30 (2017) · Zbl 1411.93193 |
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.
