Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals
Volume 11, Issue 5, pp 602--612
http://dx.doi.org/10.22436/jnsa.011.05.02
Publication Date: March 28, 2018
Submission Date: November 07, 2017
Revision Date: January 29, 2018
Accteptance Date: March 01, 2018
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Authors
Huan Zhang
- Department of Mathematics, YangZhou University, Jiangsu, 225002, China.
Wenbing Zhang
- Department of Mathematics, YangZhou University, Jiangsu, 225002, China.
Zhi Li
- Business School, SiChuan University, SiChuan, 610044, China.
Abstract
This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval
and therefore the proposed impulsive strength-dependent average impulsive
interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.
Share and Cite
ISRP Style
Huan Zhang, Wenbing Zhang, Zhi Li, Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 602--612
AMA Style
Zhang Huan, Zhang Wenbing, Li Zhi, Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals. J. Nonlinear Sci. Appl. (2018); 11(5):602--612
Chicago/Turabian Style
Zhang, Huan, Zhang, Wenbing, Li, Zhi. "Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 602--612
Keywords
- Neural networks
- impulsive strength-dependent average impulsive interval
- time-varying impulse
- stability
MSC
References
-
[1]
D. Antunes, J. Hespanha, C. Silvestre, Stability of networked control systems with asynchronous renewal links: an impulsive systems approach, Automatica J. IFAC, 49 (2013), 402–413.
-
[2]
S. Arik, Stability analysis of delayed neural networks, IEEE Trans. Circuits Systems I Fund. Theory Appl., 47 (2000), 1089–1092.
-
[3]
C. Briat , Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints, Automatica, 49 (2013), 3449–3457.
-
[4]
C. Briat , Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems, Nonlinear Anal. Hybrid Syst., 24 (2017), 198–226.
-
[5]
C. Briat, A. Seuret, A looped-functional approach for robust stability analysis of linear impulsive systems, Systems Control Lett., 61 (2012), 980–988.
-
[6]
C. Briat, A. Seuret , Convex dwell-time characterizations for uncertain linear impulsive systems, IEEE Trans. Automatic Control, 57 (2012), 3241–3246.
-
[7]
T. Chen, Global exponential stability of delayed Hopfield neural networks , Neural Netw., 14 (2001), 977–980.
-
[8]
W.-H. Chen, Z. Ruan, W. X. Zheng, Stability and l2-gain analysis for impulsive delay systems: An impulse-timedependent discretized lyapunov functional method, Automatica J. IFAC, 86 (2017), 129–137.
-
[9]
W.-H. Chen, W. X. Zheng , Global exponential stability of impulsive neural networks with variable delay: an LMI approach, IEEE Trans. Circuits Syst. I. Reg. Pap., 56 (2009), 1248–1259.
-
[10]
S. R. Chu, R. Shoureshi, M. Tenorio, Neural networks for system identification, IEEE Control Syst. Mag., 10 (1990), 31–35.
-
[11]
M. A. Davó, A. Baños, F. Gouaisbaut, S. Tarbouriechc, A. Seuret, Stability analysis of linear impulsive delay dynamical systems via looped-functionals, Automatica J. IFAC, 81 (2017), 107–114.
-
[12]
R. Goebel, R. G. Sanfelice, A. R. Teel , Hybrid dynamical systems. modeling, stability, and robustness, Princeton University Press, New Jersey (2012)
-
[13]
Z. Guo, J. Wang, Z. Yan, Attractivity analysis of memristor-based cellular neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 704–717.
-
[14]
Y. He, M.-D. Ji, C.-K. Zhang, M. Wu , Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality, Neural Netw., 77 (2016), 80–86.
-
[15]
W. He, F. Qian, J. Cao , Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control, Neural Netw., 85 (2017), 1–9.
-
[16]
M.-J. Hu, J.-W. Xiao, R.-B. Xiao, W.-H. Chen, Impulsive effects on the stability and stabilization of positive systems with delays, J. Franklin Inst., 354 (2017), 4034–4054.
-
[17]
Y. Kao, C. Wang, L. Zhang, Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction- Diffusion Cohen-Grossberg Neural Networks, Neural Process. Lett., 38 (2013), 321–346.
-
[18]
H. R. Karimi, H. Gao, New delay-dependent exponential \(H_\infty\) synchronization for uncertain neural networks with mixed time delays, IEEE Trans. Syst., Man, Cybern. B, Cybern., 40 (2010), 173–185.
-
[19]
C. Li, S. Wu, G. G. Feng, X. Liao , Stabilizing Effects of Impulses in Discrete-Time Delayed Neural Networks, IEEE Trans. Neural Netw., 22 (2011), 323–329.
-
[20]
X. Li, X. Zhang, S. Song, Effect of delayed impulses on input-to-state stability of nonlinear systems, Automatica J. IFAC, 76 (2017), 378–382.
-
[21]
Y. Liu, Z. Wang, X. Liu , Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Netw., 19 (2006), 667–675.
-
[22]
J. Louisell, New examples of quenching in delay differential equations having time-varying delay , in Proceedings of the 4th European Control Conference, (1999)
-
[23]
J. Lu, D. W. C. Ho, J. Cao, A unified synchronization criterion for impulsive dynamical networks, Automatica J. IFAC, 46 (2010), 1215–1221.
-
[24]
K. Mathiyalagan, H. Su, P. Shi, R. Sakthivel , Exponential \(H_\infty\) filtering for discrete-time switched neural networks with random delays, IEEE Trans. Cybern., 45 (2015), 676–687.
-
[25]
S. R. Naidu, E. Zafiriou, T. J. McAvoy , Use of neural networks for sensor failure detection in a control system, IEEE Control Syst. Mag., 10 (1990), 49–55.
-
[26]
A. Papachristodoulou, M. Peet, S. I. Niculescu, Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching, Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 2007 (2007), 2117–2122.
-
[27]
A. Seuret, C. Prieur, S. Tarbouriech, L. Zaccarian, Event-triggered control via reset control systems framework, IFACPapersOnLine, 49 (2016), 170–175.
-
[28]
Q. Song, H. Yan, Z. Zhao, Y. Liu, Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays, Neural Netw., 81 (2016), 1–10.
-
[29]
Y. Tang, H. Gao, J. Kurths, Multiobjective identification of controlling areas in neuronal networks, IEEE/ACM Trans. Comput. Biol. Bioinform., 10 (2013), 708–720.
-
[30]
Y. Tang, H. Gao, J. Kurths, Robust \(H_\infty\) self-triggered control of networked systems under packet dropouts, IEEE Transactions on Cybernetics, 46 (2016), 3294–3305.
-
[31]
Y. Tang, H. Gao, J. Lu, J. Kurths, Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1804–1815.
-
[32]
Y. Tang, Z. Wang, H. Gao, H. Qiao, J. Kurths , On controllability of neuronal networks with constraints on the average of control gains, IEEE Trans. Cybern., 44 (2014), 2670–2681.
-
[33]
H. Wang, S. Duan, C. Li, L. Wang, T. Huang, Stability of impulsive delayed linear differential systems with delayed impulses, J. Franklin Inst., 352 (2015), 3044–3068.
-
[34]
W. Wang, A. R. Teel, D. Nešić , Analysis for a class of singularly perturbed hybrid systems via averaging, Automatica J. IFAC, 48 (2012), 1057–1068.
-
[35]
X. Wu, Y. Tang, W. Zhang, Input-to-state stability of impulsive stochastic delayed systems under linear assumptions, Automatica J. IFAC, 66 (2016), 195–204.
-
[36]
Y. Xia, C. Sun, W. X. Zheng, Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration, IEEE Trans. Neural Netw. Learn. Syst., 23 (2012), 812–820.
-
[37]
X. Zhang, C. Li, T. Huang, Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses, Neural Netw., 93 (2017), 176–184.
-
[38]
W. Zhang, Y. Tang, J.-A. Fang, X. Wu , Stability of delayed neural networks with time-varying impulses, Neural Netw., 36 (2012), 59–63.
-
[39]
W. Zhang, Y. Tang, Q. Miao, W. Du, Exponential synchronization of coupled switched neural networks with modedependent impulsive effects, IEEE Trans. Neural Netw. Learn. Syst., 24 (2013), 1316–1326.
-
[40]
W. Zhang, Y. Tang, Q. Miao, J.-A. Fang, Synchronization of stochastic dynamical networks under impulsive control with time delays, IEEE Trans. Neural Netw. Learn. Syst., 25 (2014), 1758–1768.
-
[41]
W. Zhang, Y. Tang, X. Wu, J.-A. Fang, Synchronization of nonlinear dynamical networks with heterogeneous impulses, IEEE Trans. Circuits Syst. I, Reg. Pap., 61 (2014), 1220–1228.
-
[42]
X. Zhao, L. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode-dependent average dwell time, IEEE Trans. Automat. Control, 57 (2012), 1809–1815.
-
[43]
S. Zhu, M. Shen, C.-C. Lim , Robust input-to-state stability of neural networks with Markovian switching in presence of random disturbances or time delays, Neurocomputing, 249 (2017), 245–252.