Dissipativity analysis of neutral-type memristive neural network with two additive time-varying and leakage delays. (English) Zbl 1458.92009
Summary: In this paper, we offer an approach about the dissipativity of neutral-type memristive neural networks (MNNs) with leakage, additive time, and distributed delays. By applying a suitable Lyapunov-Krasovskii functional (LKF), some integral inequality techniques, linear matrix inequalities (LMIs) and free-weighting matrix method, some new sufficient conditions are derived to ensure the dissipativity of the aforementioned MNNs. Furthermore, the global exponential attractive and positive invariant sets are also presented. Finally, a numerical simulation is given to illustrate the effectiveness of our results.
MSC:
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 34K40 | Neutral functional-differential equations |
Keywords:
neutral-type memristive neural networks; Lyapunov-Krasovskii functional; dissipativity; mixed delaysReferences:
| [1] | Wang, Z., Liu, Y., Liu, X.: On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4-6), 299-308 (2005) · Zbl 1345.92017 · doi:10.1016/j.physleta.2005.07.025 |
| [2] | Egmont-Petersen, M., Ridder, D.D., Handels, H.: Image processing with neural networks—a review. Pattern Recognit. 35(10), 2279-2301 (2002) · Zbl 1006.68884 · doi:10.1016/S0031-3203(01)00178-9 |
| [3] | Chua, L.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507-519 (1971) · doi:10.1109/TCT.1971.1083337 |
| [4] | Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80-83 (2008) · doi:10.1038/nature06932 |
| [5] | Cantley, K.D., Subramaniam, A., Stiegler, H.J., Chapman, R.A., Vogel, E.M.: Neural learning circuits utilizing nano-crystalline silicon transistors and memristors. IEEE Trans. Neural Netw. Learn. Syst. 23(4), 565-573 (2012) · doi:10.1109/TNNLS.2012.2184801 |
| [6] | Ding, S., Wang, Z., Zhang, H.: Dissipativity analysis for stochastic memristive neural networks with time-varying delays: a discrete-time case. IEEE Trans. Neural Netw. Learn. Syst. 29(3), 618-630 (2018) · doi:10.1109/TNNLS.2016.2631624 |
| [7] | Cheng, J., Park, J.H., Cao, J., Zhang, D.: Quantized \(H∞{H^{\infty }}\) filtering for switched linear parameter-varying systems with sojourn probabilities and unreliable communication channels. Inf. Sci. 466, 289-302 (2018) · Zbl 1448.93323 · doi:10.1016/j.ins.2018.07.048 |
| [8] | Zhang, D., Cheng, J., Park, J.H., Cao, J.: Robust \(H∞{H^{\infty }}\) control for nonhomogeneous Markovian jump systems subject to quantized feedback and probabilistic measurements. J. Franklin Inst. 355(15), 6992-7010 (2018) · Zbl 1398.93109 · doi:10.1016/j.jfranklin.2018.07.011 |
| [9] | Sun, J., Chen, J.: Stability analysis of static recurrent neural networks with interval time-varying delay. Appl. Math. Comput. 221(9), 111-120 (2013) · Zbl 1329.93119 |
| [10] | Sun, Y., Cui, B.T.: Dissipativity analysis of neural networks with time-varying delays. Neurocomputing 168, 741-746 (2015) · doi:10.1016/j.neucom.2015.05.050 |
| [11] | Li, C., Feng, G.: Delay-interval-dependent stability of recurrent neural networks with time-varying delay. Neurocomputing 72, 1179-1183 (2009) · doi:10.1016/j.neucom.2008.02.011 |
| [12] | Lv, X., Li, X.: Delay-dependent dissipativity of neural networks with mixed non-differentiable interval delays. Neurocomputing 267, 85-94 (2017) · doi:10.1016/j.neucom.2017.04.059 |
| [13] | Wei, H., Li, R., Chen, C., Tu, Z.: Extended dissipative analysis for memristive neural networks with two additive time-varying delay components. Neurocomputing 216, 429-438 (2016) · doi:10.1016/j.neucom.2016.07.054 |
| [14] | Zeng, X., Xiong, Z., Wang, C.: Hopf bifurcation for neutral-type neural network model with two delays. Appl. Math. Comput. 282, 17-31 (2016) · Zbl 1410.37087 |
| [15] | Xu, C., Li, P., Pang, Y.: Exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays. Neural Comput. 28(12), 1-31 (2016) · Zbl 1482.34199 · doi:10.1162/NECO_a_00895 |
| [16] | Zhang, Y., Gu, D.W., Xu, S.: Global exponential adaptive synchronization of complex dynamical networks with neutral-type neural network nodes and stochastic disturbances. IEEE Trans. Circuits Syst. I, Regul. Pap. 60(10), 2709-2718 (2013) · doi:10.1109/TCSI.2013.2249151 |
| [17] | Brogliato, B., Maschke, B., Lozano, R., Egeland, O.: Dissipative Systems Analysis and Control. Springer, Berlin (2007) · Zbl 1121.93002 · doi:10.1007/978-1-84628-517-2 |
| [18] | Huang, Y., Ren, S.: Passivity and passivity-based synchronization of switched coupled reaction – diffusion neural networks with state and spatial diffusion couplings. Neural Process. Lett. 5, 1-17 (2017) |
| [19] | Fu, Q., Cai, J., Zhong, S., Yu, Y.: Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays. Neurocomputing 275, 747-757 (2018) · doi:10.1016/j.neucom.2017.09.014 |
| [20] | Willems, J.C.: Dissipative dynamical systems part I: general theory. Arch. Ration. Mech. Anal. 45(5), 321-351 (1972) · Zbl 0252.93002 · doi:10.1007/BF00276493 |
| [21] | Hong, D., Xiong, Z., Yang, C.: Analysis of adaptive synchronization for stochastic neutral-type memristive neural networks with mixed time-varying delays. Discrete Dyn. Nat. Soc. 2018, 8126127 (2018) · Zbl 1417.93168 · doi:10.1155/2018/8126127 |
| [22] | Cheng, J., Park, J.H., Karimi, H.R., Shen, H.: A flexible terminal approach to sampled-data exponentially synchronization of Markovian neural networks with time-varying delayed signals. IEEE Trans. Cybern. 48(8), 2232-2244 (2018) · doi:10.1109/TCYB.2017.2729581 |
| [23] | Zhang, D., Cheng, J., Cao, J., Zhang, D.: Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties. Appl. Math. Comput. 344-345, 230-242 (2019) · Zbl 1428.93129 |
| [24] | 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 Netw. 104, 93-103 (2018) · Zbl 1441.93334 · doi:10.1016/j.neunet.2018.04.010 |
| [25] | Duan, L., Huang, L.: Global dissipativity of mixed time-varying delayed neural networks with discontinuous activations. Commun. Nonlinear Sci. Numer. Simul. 19(12), 4122-4134 (2014) · Zbl 1470.92021 · doi:10.1016/j.cnsns.2014.03.024 |
| [26] | Tu, Z., Cao, J., Alsaedi, A., Alsaadi, F.: Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw. 88, 125-133 (2017) · Zbl 1461.94106 · doi:10.1016/j.neunet.2017.01.004 |
| [27] | Manivannan, R., Cao, Y.: Design of generalized dissipativity state estimator for static neural networks including state time delays and leakage delays. J. Franklin Inst. 355, 3990-4014 (2018) · Zbl 1390.93607 · doi:10.1016/j.jfranklin.2018.01.051 |
| [28] | Xiao, J., Zhong, S., Li, Y.: Relaxed dissipativity criteria for memristive neural networks with leakage and time-varying delays. Neurocomputing 171, 708-718 (2016) · doi:10.1016/j.neucom.2015.07.029 |
| [29] | Samidurai, R., Sriraman, R.: Robust dissipativity analysis for uncertain neural networks with additive time-varying delays and general activation functions. Math. Comput. Simul. 155, 201-216 (2019) · Zbl 1540.93095 · doi:10.1016/j.matcom.2018.03.010 |
| [30] | Lin, W.J., He, Y., Zhang, C., Long, F., Wu, M.: Dissipativity analysis for neural networks with two-delay components using an extended reciprocally convex matrix inequality. Inf. Sci. 450, 169-181 (2018) · Zbl 1448.93120 · doi:10.1016/j.ins.2018.03.021 |
| [31] | Aubin, J.P., Cellina, A.: Differential Inclusions. Springer, Berlin (1984) · Zbl 0538.34007 · doi:10.1007/978-3-642-69512-4 |
| [32] | Arscott, F.M.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic, Amsterdam (1988) · Zbl 0664.34001 |
| [33] | Filippov, A.F.: Classical solutions of differential equations with multi-valued right-hand side. SIAM J. Control Optim. 5(4), 609-621 (1967) · Zbl 0238.34010 · doi:10.1137/0305040 |
| [34] | Song, Q., Cao, J.: Global dissipativity analysis on uncertain neural networks with mixed time-varying delays. Chaos 18, 043126 (2008) · Zbl 1309.92017 · doi:10.1063/1.3041151 |
| [35] | Liao, X., Wang, J.: Global dissipativity of continuous-time recurrent neural networks with time delay. Phys. Rev. E 68(1 Pt 2), 016118 (2003) |
| [36] | Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49, 2860-2866 (2013) · Zbl 1364.93740 · doi:10.1016/j.automatica.2013.05.030 |
| [37] | Wang, Z., Liu, Y., Fraser, K., Liu, X.: Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354(4), 288-297 (2006) · Zbl 1181.93068 · doi:10.1016/j.physleta.2006.01.061 |
| [38] | Kwon, O.M., Lee, S.M., Park, J.H., Cha, E.J.: New approaches on stability criteria for neural networks with interval time-varying delays. Appl. Math. Comput. 218(19), 9953-9964 (2012) · Zbl 1253.34066 |
| [39] | 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 · doi:10.1016/j.automatica.2010.10.014 |
| [40] | Xin, Y., Li, Y., Cheng, Z., Huang, X.: Global exponential stability for switched memristive neural networks with time-varying delays. Neural Netw. 80, 34-42 (2016) · Zbl 1417.34183 · doi:10.1016/j.neunet.2016.04.002 |
| [41] | Guo, Z., Wang, J., Yan, Z.: Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw. 48, 158-172 (2013) · Zbl 1297.93129 · doi:10.1016/j.neunet.2013.08.002 |
| [42] | Nagamani, G., Joo, Y.H., Radhika, T.: Delay-dependent dissipativity criteria for Markovian jump neural networks with random delays and incomplete transition probabilities. Nonlinear Dyn. 91(4), 2503-2522 (2018) · Zbl 1392.93041 · doi:10.1007/s11071-017-4028-6 |
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