Abstract
The problem of finite-time stabilization (FTS) for static neural networks (SNNs) with leakage delay and time-varying delay is investigated in this paper. By introducing an auxiliary function and utilizing the Lyapunov stability theory, we derive some sufficient criteria for FTS in terms of linear matrix inequalities (LMIs). Two feedback controllers are designed based on two different Lyapunov functions, which can be easily solved via MATLAB LMI toolbox, to guarantee the FTS for the SNNs. Finally, two numerical examples are given to illustrate the efficiency of our results.
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References
Cohen M, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern B 13:815–826
Chua L, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35:1257–1272
Trentin E, Schwenker F, Gayar N, Abbas H (2018) Off the mainstream: advances in neural networks and machine learning for pattern recognition. Neural Process Lett 48:643–648
Kumar S, Raja R, Anthoni S, Cao J, Tu Z (2018) Robust finite-time non-fragile sampled-data control for T–S fuzzy flexible spacecraft model with stochastic actuator faults. Appl Math Comput 321:483–497
Xu Z, Qiao H, Peng J, Zhang B (2004) A comparative study of two modeling approaches in neural networks. Neural Netw 17:73–85
Hopfield J (1982) Neural networks and physical systems with emergent collective computational abilities. Proc USA Natl Acad Sci 79:2554–2558
Pineda F (1987) Generalization of back-propagation to recurrent neural networks. Phys Rev Lett 59:2229
Song Q, Yu Q, Zhao Z, Liu Y, Alsaadi F (2018) Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties. Neural Netw 103:55–62
Feng L, Cao J, Liu L (2018) Stability analysis in a class of Markov switched stochastic Hopfield neural networks. Neural Process Lett. https://doi.org/10.1007/s11063-018-9912-7
Wu B, Liu Y, Lu J (2012) New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays. Math Comput Model 55:837–843
Zhang X, Han Q (2018) State estimation for static neural networks with time-varying delays based on an improved reciprocally convex inequality. IEEE Trans Neural Netw Learn Syst 29:1376–1381
Zhang X, Lv X, Li X (2017) Sampled-data based lag synchronization of chaotic delayed neural networks with impulsive control. Nonlinear Dyn 90:2199–2207
Al-Darabsah I, Yuan Y (2016) A time-delayed epidemic model for Ebola disease transmission. Appl Math Comput 290:307–326
Yang X, Song Q, Cao J, Lu J (2019) Synchronization of coupled Markovian reaction–diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst 30:951–958
Guo X, Lu J, Alsaedi A, Alsaadi F (2018) Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays. Phys A Stat Mech Appl 495:488–497
Yang D, Li X, Qiu J (2019) Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonlinear Anal Hybrid Syst 32:294–305
Liu B, Hill D, Sun Z (2018) Input-to-state-KL-stability with criteria for a class of hybrid dynamical systems. Appl Math Comput 326:124–140
Li X, Wu J (2016) Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica 64:63–69
Zhou B (2018) Improved Razumikhin and Krasovskii approaches for discrete-time time-varying time-delay systems. Automatica 91:256–269
Li X, Yang X, Huang T (2019) Persistence of delayed cooperative models: impulsive control method. Appl Math Comput 342:130–146
Yang X, Li X, Xi Q, Duan P (2018) Review of stability and stabilization for impulsive delayed systems. Math Biosci Eng 15:1495–1515
Sowmiya C, Raja R, Cao J, Rajchakit G, Alsaedi A (2017) Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay. Adv Differ Equ 2017:318
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
Hu M, Cao J, Hu A (2014) Exponential stability of discrete-time recurrent neural networks with time-varying delays in the leakage terms and linear fractional uncertainties. IMA J Math Control Inf 31:345–362
Li X, Rakkiyappan R (2013) Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term. Neural Comput Appl 22:203–219
Dorato P, Short time stability in linear time-varying systems. In: Proceeding of IRE international convention record (1961)
Lv X, Li X (2017) Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications. ISA Trans 70:30–36
Wu Y, Cao J, Alofi A, AL-Mazrooei A, Elaiw A (2015) Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay. Neural Netw 69:135–143
Hu J, Sui G, Lv X, Li X (2018) Fixed-time control of delayed neural networks with impulsive perturbations. Nonlinear Anal Model Control 23:904C920
Li R, Cao J (2018) Finite-time and fixed-time stabilization control of delayed memristive neural networks: robust analysis technique. Neural Process Lett 47:1077–1096
Liu X, Cao J, Yu W, Song Q (2016) Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern 46:2360–2371
Xu C, Li P (2018) On finite-time stability for fractional-order neural networks with proportional delays. Neural Process Lett. https://doi.org/10.1007/s11063-018-9917-2
Qin S, Xue X (2009) Global exponential stability and global convergence in finite time of neural networks with discontinuous activations. Neural Process Lett 29:189–204
Wu Y, Cao J, Li Q, Alsaedi A, Alsaadi F (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139
Zhang X, Li X, Cao J, Miaadi F (2018) Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty. J Frankl Inst 355:5394–5413
Rajavel S, Samidurai R, Cao J, Alsaedi A, Ahmad B (2017) Finite-time non-fragile passivity control for neural networks with time-varying delay. Appl Math Comput 297:145–158
Li R, Cao J (2017) Finite-time stability analysis for Markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Trans Neural Netw Learn Syst 28:2924–2935
Lee W, Lee S, Park P (2017) A combined reciprocal convexity approach for stability analysis of static neural networks with interval time-varying delays. Neurocomputing 221:168–177
Senthilraj S, Raja R, Zhu Q, Samidurai R, Yao Z (2016) New delay-interval-dependent stability criteria for static neural networks with time-varying delays. Neurocomputing 186:1–7
Wu Z, Lam J, Su H, Chu J (2012) Stability and dissipativity analysis of static neural networks with time delay. IEEE Trans Neural Netw Learn Syst 23:199–210
Moulay E, Dambrine M, Yeganefar N, Perruquetti W (2008) Finite-time stability and stabilization of time-delay systems. Syst Control Lett 57:561–566
Berman A, Plemmons R (1979) Nonnegative matrices in the mathematical science. Academic press, New York
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This work was supported by National Natural Science Foundation of China (61673247) and NSERC of Canada (203786 46310 2000) (YY). The paper has not been presented at any conference.
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Zhang, X., Yuan, Y. & Li, X. Finite-Time Stabilization for Static Neural Networks with Leakage Delay and Time-Varying Delay. Neural Process Lett 51, 67–81 (2020). https://doi.org/10.1007/s11063-019-10065-1
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DOI: https://doi.org/10.1007/s11063-019-10065-1