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Passivity Analysis of Non-autonomous Discrete-Time Inertial Neural Networks with Time-Varying Delays

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Abstract

This paper addresses the passivity problem for delayed non-autonomous discrete-time inertial neural networks (NDINN), including the discrete-time switched inertial neural networks (DSINN) with state-dependent discontinuous right-hand side as its special case. First, we take a linear transformation to transform the original network into first-order difference equations. Second, by utilizing the Lyapunov direct method and with the help of the property of maximum singular value, we present a passivity criterion for the NDINN with delay-dependent linear matrix inequalities. Combining with the characteristic function method, the proposed analytical approach for NDINN is further extended to the DSINN. Finally, two simulation examples validate the efficacy of the analytical results.

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References

  1. Wang J, Jiang H, Ma T, Hu C (2018) Delay-dependent dynamical analysis of complex-valued memristive neural networks: continuous-time and discrete-time cases. Neural Netw 101:33–46

    Article  MATH  Google Scholar 

  2. Ding S, Wang Z, Zhang H (2018) Dissipativity analysis for stochastic memristive neural networks with time-varying delays: a discrete-time case. IEEE Trans Neural Netw Learn Syst 29:618–630

    Article  MathSciNet  Google Scholar 

  3. Harrer H, Nossek J (1992) Discrete-time cellular neural networks. Int J Circuit Theory Appl 20:453–467

    Article  MATH  Google Scholar 

  4. Shen T, Petersen L (2016) Linear threshold discrete-time recurrent neural networks: stability and globally attractive sets. IEEE Trans Autom Control 61:2650–2656

    Article  MathSciNet  MATH  Google Scholar 

  5. Sowmiya C, Raja R, Cao J, Li X, Rajchakit G (2018) Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: An exponential stability problem. J Franklin Inst 355:4404–4435

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu H, Wang Z, Shen B, Huang T, Alsaadi F (2018) Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays. Neural Netw 102:1–9

    Article  MATH  Google Scholar 

  7. Ma Z, Sun G, Liu D, Xing X (2016) Dissipativity analysis for discrete-time fuzzy neural networks with leakage and time-varying delays. Neurocomputing 175:579–584

    Article  Google Scholar 

  8. Song Q, Zhao Z, Liu Y (2015) Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168:1044–1050

    Article  Google Scholar 

  9. Ping Z, Hu H, Huang Y, Ge S, Lu J (2018) Discrete-time neural network approach for tracking control of spherical inverted pendulum. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2018.2834560

  10. Rubio J (2018) Discrete time control based in neural networks for pendulums. Appl Soft Comput 68:821–832

    Article  Google Scholar 

  11. Hien L, Son D, Trinh H (2018) On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE Trans Neural Netw Learn Syst 29:225–231

    Article  MathSciNet  Google Scholar 

  12. Wang L, Shen Y, Zhang G (2016) Synchronization of a class of switched neural networks with time-varying delays via nonlinear feedback control. IEEE Trans Cybern 46:2300–2310

    Article  Google Scholar 

  13. Wang H, Liu Z, He Y (2019) Exponential stability criterion of the switched neural networks with time-varying delay. Neurocomputing 331:1–9

    Article  Google Scholar 

  14. Wei X, Zhou D, Zhang Q (2009) On asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks. Comput Math Appl 57:1938–1942

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang Z, Mohamod S, Bin H (2010) Multiperiodicity analysis and numerical simulation of discrete-time transiently chaotic non-autonomous neural networks with time-varying delays. Commun Nonlinear Sci Numer Simulat 15:1348–1357

    Article  MathSciNet  MATH  Google Scholar 

  16. Zou L, Zhou Z (2006) Periodic solutions for nonautonomous discrete-time neural networks. Appl Math Lett 19:174–185

    Article  MathSciNet  MATH  Google Scholar 

  17. Mauro A, Conti F, Dodge F, Schor R (1970) Subthreshold behavior and phenomenological impedance of the squid giant axon. J Gen Physiol 55:497–523

    Article  Google Scholar 

  18. Ashmore J, Attwell D (1985) Models for electrical tuning in hair cells. Proc R Soc Lond B 226:325–344

    Article  Google Scholar 

  19. Angelaki D, Correia M (1991) Models of membrane resonance in pigeon semicircular canal type II hair cells. Biol Cybern 65:1–10

    Article  Google Scholar 

  20. Koch C (1984) Cable theory in neurons with active, linearized membranes. Biol Cybern 50:15–33

    Article  Google Scholar 

  21. Babcock K, Westervelt R (1986) Stability and dynamics of simple electronic neural networks with added inertial. Phys D 23:464–469

    Article  Google Scholar 

  22. Wheeler D, Schieve W (1997) Stability and chaos in an inertial two-neuron system. Phys D 105:267–284

    Article  MATH  Google Scholar 

  23. Li C, Chen G, Liao X, Yu J (2004) Hopf bifurcation and chaos in a single inertial neuron model with time delay. Eur Phys J B 41:337–343

    Article  Google Scholar 

  24. Ge J, Xu J (2013) Hopf bifurcation and chaos in an inertial neuron system with coupled delay. Sci China Technol Sci 56:2299–2309

    Article  Google Scholar 

  25. Wang J, Tian L (2017) Global Lagrange stability for inertial neural networks with mixed time varying delays. Neurocomputing 235:140–146

    Article  Google Scholar 

  26. Zhang G, Zeng Z (2018) Exponential stability for a class of memristive neural networks with mixed time-varying delays. Appl Math Comput 321:544–554

    MathSciNet  MATH  Google Scholar 

  27. Tu Z, Cao J, Hayat T (2016) Global exponential stability in lagrange sense for inertial neural networks with time-varying delays. Neurocomputing 171:524–531

    Article  Google Scholar 

  28. Tu Z, Cao J, Hayat T (2016) Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks. Neural Netw 75:47–55

    Article  MATH  Google Scholar 

  29. Rakkiyappan R, UdhayaKumari E, Chandrasekar A, Krishnasamy R (2016) Synchronization and periodicity of coupled inertial memristive neural networks with supremums. Neurocomputing 214:739–749

    Article  Google Scholar 

  30. Li X, Li X, Hu C (2017) Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw 96:91–100

    Article  MATH  Google Scholar 

  31. Xiao Q, Huang T, Zeng Z (2019) Global exponential stability and synchronization for discrete-Time inertial neural networks with time delays: a timescale approach. IEEE Trans Neural Netw Learn Syst 30:1854–1866

    Article  MathSciNet  Google Scholar 

  32. Willems J (1972) Dissipative dynamical systemspart I: general theory. Arch Rational Mech Anal 45:321–351

    Article  MathSciNet  MATH  Google Scholar 

  33. Willems J (1972) Dissipative dynamical systemspart II: linear systems with quadratic supply rates. Arch Rational Mech Anal 45:352–393

    Article  MathSciNet  MATH  Google Scholar 

  34. Ding K, Zhu Q, Liu L (2019) Extended dissipativity stabilization and synchronization of uncertain stochastic reaction–diffusion neural networks via intermittent non-fragile control. J Frankl Inst 356:11690–11715

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhu Q, Kumar S, Raja R, Rihan F (2019) Extended dissipative analysis for aircraft flight control systems with random nonlinear actuator fault via non-fragile sampled-data control. J Frankl Inst 356:8610–8624

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhu Q, Saravanakumar T, Gomathi S, Anthoni S (2019) Finite-time extended dissipative based optimal guaranteed cost resilient control for switched neutral systems with stochastic actuator failures. IEEE Access 7:90289–90303

    Article  Google Scholar 

  37. Xiao Q, Huang Z, Zeng Z (2019) Passivity analysis for memristor-based inertial neural networks with discrete and distributed delays. IEEE Trans Syst Man Cybern Syst 49:375–385

    Article  Google Scholar 

  38. Wan P, Jian J (2018) Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays. ISA Trans 74:88–98

    Article  Google Scholar 

  39. Xiao Q, Huang T, Zeng Z (2018) Passivity and passification of fuzzy memristive inertial neural networks on time scales. IEEE Trans Fuzzy Syst 26:3342–3355

    Article  Google Scholar 

  40. Rakkiyappan R, Chandrasekar A, Cao J (2015) Passivity and passification of memristor-based recurrent neural networks with additive time-varying delays. IEEE Trans Neural Netw Learn Syst 26:2043–2057

    Article  MathSciNet  Google Scholar 

  41. Guo Z, Wang J, Yan Z (2014) Passivity and passification of memristor-based recurrent neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25:2099–2109

    Article  Google Scholar 

  42. Zhu J, Zhang Q, Yuan Z (2010) Delay-dependent passivity criterion for discrete-time delayed standard neural network model. Neurocomputing 73:1384–1393

    Article  MATH  Google Scholar 

  43. Zhu X, Yang G (2008) Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay. In: American control conference, pp 1644–1649

  44. Chen J, Lu J, Xu S (2016) Summation inequality and its application to stability analysis for time-delay systems. IET Control Theory Appl 10:391–395

    Article  MathSciNet  Google Scholar 

  45. Xiong L, Cheng J, Cao J, Liu Z (2018) Novel inequality with application to improve the stability criterion for dynamical systems with two additive time-varying delays. Appl Math Comput 321:672–688

    MathSciNet  MATH  Google Scholar 

  46. Zhang H, Qiu Z, Xiong L, Jiang G (2019) Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality. Int J Syst Sci 50:1–19

    Article  MathSciNet  Google Scholar 

  47. Wu T, Xiong L, Cao J, Liu Z, Zhang H (2018) New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters. J Franklin Inst 355:8462–8483

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhu Q, Yang X, Wang H (2010) Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. J Franklin Inst 347:1489–1510

    Article  MathSciNet  MATH  Google Scholar 

  49. Zhu Q (2019) Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Autom Control 64:3764–3771

    Article  MathSciNet  MATH  Google Scholar 

  50. Zhu Q, Wang H (2018) Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function. Automatica 87:166–175

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Automation, Xiamen University, Xiamen, 361005, China

    Xuan Chen & Dongyun Lin

  2. School of Physics and Electronic Science, Guizhou Normal University, Guiyang, 550025, China

    Xuan Chen

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  1. Xuan Chen
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  2. Dongyun Lin
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Correspondence to Dongyun Lin.

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This work is supported by the National Natural Science Foundation of China (61873219) .

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Chen, X., Lin, D. Passivity Analysis of Non-autonomous Discrete-Time Inertial Neural Networks with Time-Varying Delays. Neural Process Lett 51, 2929–2944 (2020). https://doi.org/10.1007/s11063-020-10235-6

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  • DOI: https://doi.org/10.1007/s11063-020-10235-6

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