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Erschienen in: Neural Processing Letters 1/2021

04.01.2021

Robust Passivity and Stability Analysis of Uncertain Complex-Valued Impulsive Neural Networks with Time-Varying Delays

verfasst von: G. Rajchakit, R. Sriraman

Erschienen in: Neural Processing Letters | Ausgabe 1/2021

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Abstract

In this article, we investigate the robust passivity and stability analysis of uncertain complex-valued impulsive neural network (UCVINN) models with time-varying delays. Many practical systems are subject to uncertainty in the real-world environments. As a result, we consider the uncertainty of norm-bounded parameters to achieve more realistic system behaviors. By using appropriate Lyapunov–Krasovskii functionals and integral inequalities, sufficient conditions for the robust passivity and global asymptotic stability of UCVINNs are derived by separating complex-valued neural networks into real and imaginary parts. The criteria are given in terms of linear matrix inequalities (LMIs) that can be checked by the MATLAB LMI toolbox. Finally, numerical simulations are presented to illustrate the merits of the obtained results.

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Literatur
1.
Zurück zum Zitat Haykin S (2002) Neural networks: a comprehensive foundation. Pearson Education, SingaporeMATH Haykin S (2002) Neural networks: a comprehensive foundation. Pearson Education, SingaporeMATH
2.
Zurück zum Zitat Cao J (2000) Global asymptotic stability of neural networks with transmission delays. Int J Syst Sci 31:1313–1316MATHCrossRef Cao J (2000) Global asymptotic stability of neural networks with transmission delays. Int J Syst Sci 31:1313–1316MATHCrossRef
3.
Zurück zum Zitat Zeng HB, He Y, Wu M, Xiao SP (2015) Stability analysis of generalized neural networks with time-varying delays via a new integral inequality. Neurocomputing 161:148–154CrossRef Zeng HB, He Y, Wu M, Xiao SP (2015) Stability analysis of generalized neural networks with time-varying delays via a new integral inequality. Neurocomputing 161:148–154CrossRef
4.
Zurück zum Zitat Zhang H, Yang F, Liu X, Zhang Q (2013) Stability analysis for neural networks with time-varying delay based on quadratic convex combination. IEEE Trans Neural Netw Learn Syst 24:513–521CrossRef Zhang H, Yang F, Liu X, Zhang Q (2013) Stability analysis for neural networks with time-varying delay based on quadratic convex combination. IEEE Trans Neural Netw Learn Syst 24:513–521CrossRef
5.
Zurück zum Zitat Hopfield J (1982) Neural Networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A 79:2554–2558MathSciNetMATHCrossRef Hopfield J (1982) Neural Networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A 79:2554–2558MathSciNetMATHCrossRef
6.
Zurück zum Zitat Wang T, Zhao S, Zhou W, Yu W (2015) Finite-time state estimation for delayed Hopfield neural networks with Markovian jump. Neurocomputing 156:193–198CrossRef Wang T, Zhao S, Zhou W, Yu W (2015) Finite-time state estimation for delayed Hopfield neural networks with Markovian jump. Neurocomputing 156:193–198CrossRef
7.
Zurück zum Zitat Wang Z, Guo Huang L, Liu X (2017) Dynamical behavior of complex-valued Hopfield neural networks with discontinuous activation functions. Neural Process Lett 45:1039–1061CrossRef Wang Z, Guo Huang L, Liu X (2017) Dynamical behavior of complex-valued Hopfield neural networks with discontinuous activation functions. Neural Process Lett 45:1039–1061CrossRef
8.
Zurück zum Zitat Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2013) Analysis on robust \(H_\infty \) performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov–Krasovskii functional. Appl Math Comput 224:108–122MathSciNetMATH Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2013) Analysis on robust \(H_\infty \) performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov–Krasovskii functional. Appl Math Comput 224:108–122MathSciNetMATH
9.
Zurück zum Zitat Zeng HB, Liu XG, Wang W, Xiao SP (2019) New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality. J Frankl Inst 356(13):7312–7321MathSciNetMATHCrossRef Zeng HB, Liu XG, Wang W, Xiao SP (2019) New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality. J Frankl Inst 356(13):7312–7321MathSciNetMATHCrossRef
10.
Zurück zum Zitat Hu B, Song Q, Li K, Zahao Z, Liu Y, Alsaadi FE (2015) Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168:1044–1050CrossRef Hu B, Song Q, Li K, Zahao Z, Liu Y, Alsaadi FE (2015) Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168:1044–1050CrossRef
11.
Zurück zum Zitat Maharajan C, Raja R, Cao J, Rajchakit G (2019) Fractional delay segments method on time-delayed recurrent neural networks with impulsive and stochastic effects: an exponential stability approach. Neurocomputing 323:277–298CrossRef Maharajan C, Raja R, Cao J, Rajchakit G (2019) Fractional delay segments method on time-delayed recurrent neural networks with impulsive and stochastic effects: an exponential stability approach. Neurocomputing 323:277–298CrossRef
12.
Zurück zum Zitat Zhang D, Jiang H, Wang J, Yu Z (2018) Global stability of complex-valued recurrent neural networks with both mixed time delays and impulsive effect. Neurocomputing 282:157–166CrossRef Zhang D, Jiang H, Wang J, Yu Z (2018) Global stability of complex-valued recurrent neural networks with both mixed time delays and impulsive effect. Neurocomputing 282:157–166CrossRef
13.
Zurück zum Zitat Hu B, Song Q, Li K, Zhao Z, Liu Y, Alsaadi FE (2018) Global \(\mu \)-synchronization of impulsive complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 307:106–116CrossRef Hu B, Song Q, Li K, Zhao Z, Liu Y, Alsaadi FE (2018) Global \(\mu \)-synchronization of impulsive complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 307:106–116CrossRef
14.
Zurück zum Zitat Subramanian K, Muthukumar P, Lakshmanan S (2018) State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties. Appl Math Comput 321:267–281MathSciNetMATH Subramanian K, Muthukumar P, Lakshmanan S (2018) State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties. Appl Math Comput 321:267–281MathSciNetMATH
15.
Zurück zum Zitat Maharajan C, Raja R, Cao J, Rajchakit G, Alsaedi A (2018) Impulsive Cohen–Grossberg BAM neural networks with mixed time-delays: an exponential stability analysis issue. Neurocomputing 275:2588–2602CrossRef Maharajan C, Raja R, Cao J, Rajchakit G, Alsaedi A (2018) Impulsive Cohen–Grossberg BAM neural networks with mixed time-delays: an exponential stability analysis issue. Neurocomputing 275:2588–2602CrossRef
16.
Zurück zum Zitat Zhu Q, Song B (2011) Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays. Nonlinear Anal Real World Appl 12:2851–2860MathSciNetMATHCrossRef Zhu Q, Song B (2011) Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays. Nonlinear Anal Real World Appl 12:2851–2860MathSciNetMATHCrossRef
17.
Zurück zum Zitat Song Q, Cao J (2012) Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dyn 67:1695–1707MathSciNetMATHCrossRef Song Q, Cao J (2012) Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dyn 67:1695–1707MathSciNetMATHCrossRef
18.
Zurück zum Zitat Xu S, Zheng WX, Zou Y (2009) Passivity analysis of neural networks with time-varying delays. IEEE Trans Circuits Syst II 56:325–329CrossRef Xu S, Zheng WX, Zou Y (2009) Passivity analysis of neural networks with time-varying delays. IEEE Trans Circuits Syst II 56:325–329CrossRef
19.
Zurück zum Zitat Chen Y, Wang H, Xue A, Lu R (2010) Passivity analysis of stochastic time-delay neural networks. Nonlinear Dyn 61(1–2):71–82MathSciNetMATHCrossRef Chen Y, Wang H, Xue A, Lu R (2010) Passivity analysis of stochastic time-delay neural networks. Nonlinear Dyn 61(1–2):71–82MathSciNetMATHCrossRef
20.
Zurück zum Zitat 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 155:57–77MathSciNetMATHCrossRef 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 155:57–77MathSciNetMATHCrossRef
21.
Zurück zum Zitat Ramasamy S, Nagamani G (2017) Dissipativity and passivity analysis for discrete-time complex-valued neural networks with leakage delay and probabilistic time-varying delays. Int J Adapt Control Signal Process 31:876–902MathSciNetMATHCrossRef Ramasamy S, Nagamani G (2017) Dissipativity and passivity analysis for discrete-time complex-valued neural networks with leakage delay and probabilistic time-varying delays. Int J Adapt Control Signal Process 31:876–902MathSciNetMATHCrossRef
22.
Zurück zum Zitat Wang S, Cao Y, Huang T, Wen S (2019) Passivity and passification of memristive neural networks with leakage term and time-varying delays. Appl Math Comput 361:294–310MathSciNetMATH Wang S, Cao Y, Huang T, Wen S (2019) Passivity and passification of memristive neural networks with leakage term and time-varying delays. Appl Math Comput 361:294–310MathSciNetMATH
23.
Zurück zum Zitat Song Q, Zhao Z, Liu Y (2015) Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159:96–104CrossRef Song Q, Zhao Z, Liu Y (2015) Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159:96–104CrossRef
24.
Zurück zum Zitat Chen X, Song Q (2013) Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing 121:254–264CrossRef Chen X, Song Q (2013) Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing 121:254–264CrossRef
25.
Zurück zum Zitat Samidurai R, Sriraman R, Zhu S (2019) Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays. Neurocomputing 338:262–273CrossRef Samidurai R, Sriraman R, Zhu S (2019) Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays. Neurocomputing 338:262–273CrossRef
26.
Zurück zum Zitat Gong W, Liang J, Kan X, Nie X (2017) Robust state estimation for delayed complex-valued neural networks. Neural Process Lett 46:1009–1029CrossRef Gong W, Liang J, Kan X, Nie X (2017) Robust state estimation for delayed complex-valued neural networks. Neural Process Lett 46:1009–1029CrossRef
27.
Zurück zum Zitat Wang Z, Huang L (2016) Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173:2083–2089CrossRef Wang Z, Huang L (2016) Global stability analysis for delayed complex-valued BAM neural networks. Neurocomputing 173:2083–2089CrossRef
28.
Zurück zum Zitat Subramanian K, Muthukumar P (2017) Global asymptotic stability of complex-valued neural networks with additive time-varying delays. Cogn Neurodyn 11:293–306CrossRef Subramanian K, Muthukumar P (2017) Global asymptotic stability of complex-valued neural networks with additive time-varying delays. Cogn Neurodyn 11:293–306CrossRef
29.
Zurück zum Zitat Zhang Z, Liu X, Guo R, Lin C (2018) Finite-time stability for delayed complex-valued BAM neural networks. Neural Process Lett 48:179–193CrossRef Zhang Z, Liu X, Guo R, Lin C (2018) Finite-time stability for delayed complex-valued BAM neural networks. Neural Process Lett 48:179–193CrossRef
30.
Zurück zum Zitat Zhang Z, Liu X, Zhou D, Lin C, Chen J, Wang H (2018) Finite-time stabilizability and instabilizability for complex-valued memristive neural networks with time delays. IEEE Trans Syst Man Cybern Syst 48:2371–2382CrossRef Zhang Z, Liu X, Zhou D, Lin C, Chen J, Wang H (2018) Finite-time stabilizability and instabilizability for complex-valued memristive neural networks with time delays. IEEE Trans Syst Man Cybern Syst 48:2371–2382CrossRef
31.
Zurück zum Zitat Tu Z, Cao J, Alsaedi A, Alsaadi FE, Hayat T (2016) Global Lagrange stability of complex-valued neural networks of neutral type with time-varying delays. Complexity 21:438–450MathSciNetCrossRef Tu Z, Cao J, Alsaedi A, Alsaadi FE, Hayat T (2016) Global Lagrange stability of complex-valued neural networks of neutral type with time-varying delays. Complexity 21:438–450MathSciNetCrossRef
32.
Zurück zum Zitat Nitta T (2003) Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Netw 16(8):1101–1105CrossRef Nitta T (2003) Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Netw 16(8):1101–1105CrossRef
33.
Zurück zum Zitat Pratap A, Raja R, Cao J, Rajchakit G, Lim CP (2019) Global robust synchronization of fractional order complex-valued neural networks with mixed time varying delays and impulses. Int J Control Autom Syst 17(2):509–520CrossRef Pratap A, Raja R, Cao J, Rajchakit G, Lim CP (2019) Global robust synchronization of fractional order complex-valued neural networks with mixed time varying delays and impulses. Int J Control Autom Syst 17(2):509–520CrossRef
34.
Zurück zum Zitat Liu D, Zhu S, Chang W (2017) Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay. Int J Syst Sci 48:1966–1977MathSciNetMATHCrossRef Liu D, Zhu S, Chang W (2017) Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay. Int J Syst Sci 48:1966–1977MathSciNetMATHCrossRef
35.
Zurück zum Zitat Samidurai R, Sriraman R, Cao J, Tu Z (2018) Effects of leakage delay on global asymptotic stability of complex-valued neural networks with interval time-varying delays via new complex-valued Jensens inequality. Int J Adapt Control Signal Process 32:1294–1312MathSciNetMATH Samidurai R, Sriraman R, Cao J, Tu Z (2018) Effects of leakage delay on global asymptotic stability of complex-valued neural networks with interval time-varying delays via new complex-valued Jensens inequality. Int J Adapt Control Signal Process 32:1294–1312MathSciNetMATH
36.
Zurück zum Zitat Liu D, Zhu S, Chang W (2017) Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays. Nonlinear Dyn 90:915–934MathSciNetMATHCrossRef Liu D, Zhu S, Chang W (2017) Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays. Nonlinear Dyn 90:915–934MathSciNetMATHCrossRef
37.
Zurück zum Zitat Sriraman R, Samidurai R (2019) Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays. Int J Syst Sci 50:1742–1756MathSciNetMATHCrossRef Sriraman R, Samidurai R (2019) Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays. Int J Syst Sci 50:1742–1756MathSciNetMATHCrossRef
38.
Zurück zum Zitat Kwon OM, Park JH (2008) Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays. J Frankl Inst 345:766–778MathSciNetMATHCrossRef Kwon OM, Park JH (2008) Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays. J Frankl Inst 345:766–778MathSciNetMATHCrossRef
39.
Zurück zum Zitat Kwon OM, Park JH (2008) New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays. Appl Math Comput 205:417–427MathSciNetMATH Kwon OM, Park JH (2008) New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays. Appl Math Comput 205:417–427MathSciNetMATH
40.
Zurück zum Zitat Samidurai R, Sriraman R, Cao J, Tu Z (2018) Nonfragile stabilization for uncertain system with interval time-varying delays via a new double integral inequality. Math Methods Appl Sci 41:6272–6287MathSciNetMATHCrossRef Samidurai R, Sriraman R, Cao J, Tu Z (2018) Nonfragile stabilization for uncertain system with interval time-varying delays via a new double integral inequality. Math Methods Appl Sci 41:6272–6287MathSciNetMATHCrossRef
41.
Zurück zum Zitat Wang Y, Zheng CD, Feng E (2013) Stability analysis of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations. Neurocomputing 119:454–461CrossRef Wang Y, Zheng CD, Feng E (2013) Stability analysis of mixed recurrent neural networks with time delay in the leakage term under impulsive perturbations. Neurocomputing 119:454–461CrossRef
42.
Zurück zum Zitat 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 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
43.
Zurück zum Zitat Ma Y, Yan H (2013) Delay-dependent non-fragile robust dissipative filtering for uncertain nonlinear stochastic singular time-delay systems with Markovian jump parameters. Adv Differ Equ 2013:135MathSciNetMATHCrossRef Ma Y, Yan H (2013) Delay-dependent non-fragile robust dissipative filtering for uncertain nonlinear stochastic singular time-delay systems with Markovian jump parameters. Adv Differ Equ 2013:135MathSciNetMATHCrossRef
44.
Zurück zum Zitat Yang S, Li C, Huang T (2016) Finite-time stabilization of uncertain neural networks with distributed time-varying delays. Neural Comput Appl 28:1155–1163CrossRef Yang S, Li C, Huang T (2016) Finite-time stabilization of uncertain neural networks with distributed time-varying delays. Neural Comput Appl 28:1155–1163CrossRef
45.
Zurück zum Zitat Guo J, Meng Z, Xiang Z (2018) Passivity analysis of stochastic memristor-based complex-valued recurrent neural networks with mixed time-varying delays. Neural Process Lett 47:1097–1113CrossRef Guo J, Meng Z, Xiang Z (2018) Passivity analysis of stochastic memristor-based complex-valued recurrent neural networks with mixed time-varying delays. Neural Process Lett 47:1097–1113CrossRef
46.
Zurück zum Zitat Cao Y, Cao Y, Wen S, Huang T, Zenga Z (2019) Passivity analysis of delayed reaction-diffusion memristor-based neural networks. Neural Netw 109:159–167MATHCrossRef Cao Y, Cao Y, Wen S, Huang T, Zenga Z (2019) Passivity analysis of delayed reaction-diffusion memristor-based neural networks. Neural Netw 109:159–167MATHCrossRef
47.
Zurück zum Zitat Velmurugan G, Rakkiyappan R, Lakshmanan S (2015) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42:517–540CrossRef Velmurugan G, Rakkiyappan R, Lakshmanan S (2015) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42:517–540CrossRef
48.
Zurück zum Zitat Zhang Z, Liu X, Chen J, Guo R, Zhou S (2017) Further stability analysis for delayed complex-valued recurrent neural networks. Neurocomputing 251:81–89CrossRef Zhang Z, Liu X, Chen J, Guo R, Zhou S (2017) Further stability analysis for delayed complex-valued recurrent neural networks. Neurocomputing 251:81–89CrossRef
49.
Zurück zum Zitat Cao Y, Sriraman R, Samidurai R (2020) Stability and stabilization analysis of nonlinear time-delay systems with randomly occurring controller gain fluctuation. Math Comput Simul 171:36–51MathSciNetCrossRef Cao Y, Sriraman R, Samidurai R (2020) Stability and stabilization analysis of nonlinear time-delay systems with randomly occurring controller gain fluctuation. Math Comput Simul 171:36–51MathSciNetCrossRef
50.
Metadaten
Titel
Robust Passivity and Stability Analysis of Uncertain Complex-Valued Impulsive Neural Networks with Time-Varying Delays
verfasst von
G. Rajchakit
R. Sriraman
Publikationsdatum
04.01.2021
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 1/2021
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-020-10401-w

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