Further results on dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties
In this paper, the problem of robust dissipativity is investigated for neural networks with both time-varying delay and randomly occurring uncertainties. The randomly occurring uncertainties are assumed to obey mutually uncorrelated Bernoulli-distributed white noise sequences. By constructing a new Lyapunov–Krasovskii functional, some improved delay-dependent dissipativity conditions are derived based on two integral inequalities, which are formulated in terms of linear matrix inequality. Furthermore, some information of activation function ignored in previous works has been taken into account in the resulting condition. The effectiveness and the improvement of the proposed approach are demonstrated by two illustrating numerical examples.
KeywordsNeural networks Time delay Randomly occurring uncertainties Dissipativity
This work of H.B. Zeng was supported by the National Natural Science Foundation of China under Grant Nos. 61304064 and 61273157. The work of J.H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2A10005201). Special thanks of Dr. J.H. Park go to N. Kim for continuous supports and encouragement on his works.
- 18.Wang, Z., Liu, Y., Fraser, K., Liu, X.: Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354, 288–297 (2006)Google Scholar
- 19.Cao, J., Yuan, K., Li, X.: Global asymptotical stability of generalized recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17, 1646–1651 (2007)Google Scholar
- 28.Feng, Z., Lam, J., Gao, H.: \(\alpha \)-dissipativity analysis of singular time-delay systems. Automatica 47, 2548–2552 (2011) Google Scholar
- 29.Hu, J., Wang, Z., Gao, H., Stergioulas, L.K.: Robust sliding mode control for discrete stochastic systems with mixed time-delays, randomly occurring uncertainties and nonlinearities. IEEE Trans. Ind. Electron. 59, 3008–3015 (2012)Google Scholar
- 33.Zeng, H.B., He, Y., Wu, M., Xiao, H.Q.: Improved conditions for passivity of neural networks with a time-varying delay. IEEE Trans. Cybern. 44, 785–792 (2014)Google Scholar