Abstract
In this paper, the problem of delay-derivative-dependent stability analysis for generalized neural networks with interval time-varying delays is considered. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, where the information on the lower and upper bounds of time delay and its derivative are fully exploited. Second, a new delay-derivative-dependent stability condition for time-varying delay systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed-decomposition approach and integral inequality approach. Third, all the conditions are presented in terms of LMIs can be easily calculated by using Matlab LMI control toolbox. Fourth, the computational complexity of newly obtained stability conditions is reduced because fewer variables are involved. Finally, four numerical examples are provided to verify the effectiveness of the proposed criteria.
Similar content being viewed by others
References
Bai YQ, Chen J (2013) New stability criteria for recurrent neural networks with interval time-varying delay. Neurocomputing 121(9):179–184
Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia
Cao J, Wang J (2003) Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circ Syst I Fundam Theory Appl 50(1):34–44
Cao Y, Samidurai R, Sriraman R (2019) Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function. Math Comput Simul 155:57–77
Du B, Lam J (2009) Stability analysis of static recurrent neural networks using delay-partitioning and projection. Neural Netw 22(4):343–347
Ge C, Hua C, Ping X (2014) New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach. IEEE Trans Neural Netw Learn Syst 25(7):1378–1383
Huang C, Liu B, Tian X, Yang L, Zhang X (2019) Global convergence on asymptotically almost periodic SICNNs with nonlinear decay functions. Neural Process Lett 49(2):625–641
Ji MD, He Y, Zhang CK, Wu M (2014) Novel stability criteria for recurrent neural networks with time-varying delay. Neurocomputing 138:383–391
Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2013) Analysis on delay-dependent stability for neural networks with time-varying delays. Neurocomputing 103(1):114–120
Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2014) New and improved results on stability of static neural networks with interval time-varying delays. Appl Math Comput 239:346–357
Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2014) On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov–Krasovskii functional. Commun Nonlinear Sci Numer Simul 19(9):3184–3201
Li T, Wang T, Song A, Fei S (2013) Combined convex technique on delay-dependent stability for delayed neural networks. IEEE Trans Neural Netw Learn Syst 24(9):1459–1466
Li XW, Gao HJ, Yu XH (2011) A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays. IEEE Trans Syst Man Cybern B Cybern 41(5):1275–1286
Liang J, Cao J (2006) A based-on LMI stability criterion for delayed recurrent neural networks. Chaos Solitons Fractal 28(1):154–160
Liu PL (2009) Robust exponential stability for uncertain time-varying delay systems with delay dependence. J Frankl Inst 346(10):958–968
Liu PL (2013) Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay. ISA Trans 52(6):711–716
Liu PL (2013) Delay-dependent robust stability analysis for recurrent neural networks with time-varying delay. Int J Innov Comput Inf Control 9(8):3341–3356
Liu PL (2013) Improved delay-dependent robust stability criteria for recurrent neural networks with time-varying delays. ISA Trans 52(1):30–35
Liu PL (2015) Further results on robust delay-range-dependent stability criteria for uncertain neural networks with interval time-varying delay. Int J Control Autom Syst 13(5):1140–1149
Liu PL (2015) Delayed-decomposition approach for absolute stability of neutral-type Lurie control systems with time-varying delays. ASME J Dyn Syst Measur Control 137:081002-1
Liu PL (2015) Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays. ISA Trans 55:92–99
Li T, Zheng WX, Lin C (2011) Delay-slope-dependent stability results of recurrent neural networks. IEEE Trans Neural Netw 22(12):2138–2143
Liu Y, Lee SM, Kwon OM, Park JH (2015) New approach to stability criteria for generalized neural networks with interval time-varying delays. Neurocomputing 149:1544–1551
Liu YM, Tian JK, Ren Z (2017) New stability analysis for generalized neural networks with interval time-varying delays. Int J Control Autom Syst 15(4):1600–1610
Park PG, Ko JW (2007) Stability and robust stability for systems with a time-varying delay. Automatica 43:1855–1858
Pradeep C, Cao Y, Murugesu R, Rakkiyappan R (2019) An event-triggered synchronization of semi-Markov jump neural networks with time-varying delays based on generalized free-weighting-matrix approach. Math Comput Simul 155:41–56
Senthilraj S, Raja R, Zhu QX, Samidurai R, Yao ZS (2016) New delay-interval-dependent stability criteria for static neural networks with time-varying delays. Neurocomputing 186:1–7
Sun J, Liu GP, Chen J, Rees D (2010) Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2):466–470
Sun J, Chen J (2013) Stability analysis of static recurrent neural networks with interval time-varying delay. Appl Math Comput 221:111–120
Wang X, Shea K, Zhong SM, Yang HL (2016) New and improved results for recurrent neural networks with interval time-varying delay. Neurocomputing 175:492–499
Xiong X, Tang R, Yang X (2018) Finite-time synchronization of memristive neural networks with proportional delay. Neural Process Lett. https://doi.org/10.1007/s11063-018-9910-9
Yang Q, Ren Q, Xie X (2014) New delay dependent stability criteria for recurrent neural networks with interval time-varying delay. ISA Trans 53(4):994–999
Yang R, Zhang Z, Shi P (2010) Exponential stability on stochastic neural networks with discrete interval and distributed delays. IEEE Trans Neural Netw 21(1):169–175
Yang X, Cao J, Yang Z (2013) Synchronization of coupled reaction- diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM J Control Optim 51(5):3486–3510
Yang XS, Song Q, Cao J, Lu JQ (2019) Synchronization of coupled Markovian reaction–diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst 3(3):951–958
Zeng H, He Y, Wu M, Zhang C (2011) Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays. IEEE Trans Neural Netw 22(5):806–812
Zhang CK, He Y, Jiang L, Wu QH, Wu M (2014) Delay-dependent stability criteria for generalized neural networks with two delay components. IEEE Trans Neural Netw Learn Syst 25(7):1263–1276
Zhang D, Cheng J, Cao J, Zhang D (2019) Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties. Appl Math Comput 344:230–242
Zhang HG, Liu ZW, Huang GB, Wang ZS (2010) Novel weighting- delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw 21(1):91–106
Zhang XM, Han QL (2011) Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw 22(8):1180–1192
Zhang XM, Han QL (2013) Novel delay-derivative-dependent stability criteria using new bounding techniques. Int J Robust Nonlinear Control 23(13):1419–1432
Zhang Y, Yue D, Tian E (2009) New stability criteria of neural networks with interval time-varying delays: a piecewise delay method. Appl Math Comput 208(1):249–259
Zhou C, Zhang W, Yang X, Xu C, Feng J (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46:271–291
Zhou X, Tian J, Ma H, Zhong S (2014) Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays. Neurocomputing 129:401–408
Zuo Z, Yang C, Wang Y (2010) A new method for stability analysis of recurrent neural networks with interval time-varying delay. IEEE Trans Neural Netw 21(2):339–344
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, PL. Improved Delay-Derivative-Dependent Stability Analysis for Generalized Recurrent Neural Networks with Interval Time-Varying Delays. Neural Process Lett 51, 427–448 (2020). https://doi.org/10.1007/s11063-019-10088-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-019-10088-8