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Neural Processing Letters

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18-08-2018

New Results on Robust Finite-Time Passivity for Fractional-Order Neural Networks with Uncertainties

Authors: Mai Viet Thuan, Dinh Cong Huong, Duong Thi Hong

Published in: Neural Processing Letters | Issue 2/2019

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Abstract

In this paper, the robust finite-time passivity for a class of fractional-order neural networks with uncertainties is considered. Firstly, the definition of finite-time passivity of fractional-order neural networks is introduced. Then, by using finite-time stability theory and linear matrix inequality approach, new sufficient conditions that ensure the finite-time passivity of the fractional-order neural network systems are derived via linear matrix inequalities which can be effectively solved by various computational tools. Finally, three numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.

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Kilbas A, Srivastava H, Trujillo J (2006) Theory and application of fractional diffrential equations. Elsevier, New York

Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffer stability. Comput Math Appl 59(5):1810–1821MathSciNetCrossRef

Kaczorek T (2011) Selected problems of fractional systems theory. Springer, BerlinCrossRef

Thuan MV, Huong DC (2018) New results on stabilization of fractional-order nonlinear systems via an LMI approach. Asian J Control. 20(4):1541–1550

Zhang S, Chen Y, Yu Y (2017) A survey of fractional-order neural networks. In: ASME 2017 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers

Wang H, Yu Y, Wen G (2014) Stability analysis of fractional-order Hopfield neural networks with time delays. Neural Netw 55:98–109CrossRef

Wang H, Yu Y, Wen G, Zhang S (2015) Stability analysis of fractional-order neural networks with time delay. Neural Process Lett 42(2):479–500CrossRef

Yang X, Li C, Song Q (2016) Mittag–Leffler stability analysis on variable-time impulsive fractional order neural networks. Neurocomputing 207:276–286CrossRef

Zhang S, Yu Y, Yu J (2017) LMI conditions for global stability of fractional-order neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2423–2433MathSciNetCrossRef

10.

Zhang S, Yo Y, Geng L (2017) Stability analysis of fractional-order Hopfield neural networks with time-varying external inputs. Neural Process Lett 45(1):223–241CrossRef

11.

Wei H, Li R, Chen C, Tu Z (2017) Stability analysis of fractional order complex-valued memristive neural networks with time delays. Neural Process Lett 45(2):379–399CrossRef

12.

Yang X, Song Q, Liu Y, Zhao Z (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26CrossRef

13.

Dinh X, Cao J, Zhao X, Alsaadi FE (2017) Finite-time stability of fractional-order complex-valued neural networks with time delays. Neural Process Lett 46(2):561–580CrossRef

14.

Dinh Z, Zeng Z, Wang L (2018) Robust finite-time stabilization of fractional-order neural networks with discontinuous and continuous activation functions under uncertainty. IEEE Trans Neural Netw Learn Syst 29(5):1477–1490

15.

Song S, Song X, Balsera IT (2018) Mixed \(H_{\infty }/\)passive projective synchronization for nonidentical uncertain fractional-order neural networks based on adaptive sliding mode control. Neural Process Lett 47(2):443–462

16.

Bao H, Park JH, Cao J (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354MathSciNetCrossRef

17.

Bao H, Park JH, Cao J (2016) Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 81:16–28CrossRef

18.

Hill D, Moylan P (1976) The stability of nonlinear dissipative systems. IEEE Trans Autom Control 21:708–711MathSciNetCrossRef

19.

Brogliato B, Maschke B, Lozano R, Egeland O (2007) Dissipative systems analysis and control: theory and applications. Springer, LondonCrossRef

20.

Mathiyalagan K, Park JH, Sakthivel R (2015) New results on passivity-based \(H_{\infty }\) control for networked cascade control systems with application to power plant boiler-turbine system. Nonlinear Anal Hybrid Syst 17:56–69

21.

Wu A, Zeng Z (2014) Passivity analysis of memristive neural networks with different memductance functions. Commun Nonlinear Sci Numer Simulat 19:274–285MathSciNetCrossRef

22.

Zeng HB, Park JH, Shen H (2015) Robust passivity analysis of neural networks with discrete and distributed delays. Neurocomputing 149:1092–1097CrossRef

23.

Velmurugan G, Rakkiyappan R, Lakshmanan S (2015) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42(3):517–540CrossRef

24.

Thuan MV, Trinh H, Hien LV (2016) New inequality-based approach to passivity analysis of neural networks with interval time-varying delay. Neurocomputing 194:301–307CrossRef

25.

Nagamani G, Radhika T (2016) Dissipativity and passivity analysis of Markovian jump neural networks with two additive time-varying delays. Neural Process Lett 44(2):571–592CrossRef

26.

Huang Y, Ren S (2017) Passivity and passivity-based synchronization of switched coupled reaction–diffusion neural networks with state and spatial diffusion couplings. Neural Process Lett 47(2):347–363

27.

Mathiyalagan K, Anbuvithya R, Sakthivel R, Park JH, Prakash P (2016) Non-fragile \(H_{\infty }\) synchronization of memristor-based neural networks using passivity theory. Neural Netw 74:85–100

28.

He S, Liu F (2014) Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems. J Franklin Inst 351(7):3782–3796MathSciNetCrossRef

29.

Qi W, Gao X, Wang J (2016) Finite-time passivity and passification for stochastic time-delayed Markovian switching systems with partly known transition rates. Circuits Syst Signal Process 35(11):3913–3934CrossRef

30.

Song J, He S (2015) Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays. Neurocomputing 159:275–281CrossRef

31.

Mathiyalagan K, Park JH, Sakthivel R (2016) Novel results on robust finite-time passivity for discrete-time delayed neural networks. Neurocomputing 177:585–593CrossRef

32.

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 297:145–158MathSciNetMATH

33.

Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187(2):777–784MathSciNetMATH

34.

Amato F, Ariola M, Dorato P (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37:1459–1463CrossRef

35.

Ma Y, Wu B, Wang YE (2016) Finite-time stability and finite-time boundedness of fractional order linear systems. Neurocomputing 173:2076–2082CrossRef

36.

Duarte-Mermoud MA, Aguila-Camacho N, JGallegos JA, Castro-Linares R (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun Nonlinear Sci Numer Simulat 22:650–659MathSciNetCrossRef

37.

Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRef

38.

Wu R, Lu Y, Chen L (2015) Finite-time stability of fractional delayed neural networks. Neurocomputing 149:700–707CrossRef

39.

Chen L, Liu C, Wu R, He Y, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27(3):549–556CrossRef

40.

Wang L, Song Q, Liu Y, Zhao Z, Alsaadi FE (2017) Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays. Neurocomputing 245:86–101CrossRef

41.

Zhang H, Ye R, Cao R, Ahmed A, Li X, Wan Y (2018) Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays. Asian J Control 20(6):1–14MathSciNetCrossRef

42.

Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256CrossRef

Title: New Results on Robust Finite-Time Passivity for Fractional-Order Neural Networks with Uncertainties
Authors: Mai Viet Thuan
Dinh Cong Huong
Duong Thi Hong
Publication date: 18-08-2018
Publisher: Springer US
Published in: Neural Processing Letters / Issue 2/2019
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-018-9902-9

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