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Locally Exponential Stability of Discrete-time Complex Networks with Impulsive Input Saturation

  • Keyu Chen
  • Chuandong LiEmail author
  • Liangliang Li
Regular Papers Control Theory and Applications
  • 15 Downloads

Abstract

In this paper, the problem of exponential stabilization for a class of discrete-time complex network with saturated impulse input is investigated. Based on the inductive method, convex analysis, and auxiliary matrix, several Lyapunov-type stability criteria are derived for exponential stability of discrete-time complex network with impulsive input saturation. Two examples are also presented to illustrate the effectiveness and the feasibility of the obtained results.

Keywords

Convex analysis discrete-time complex networks impulsive control saturated impulsive input 

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References

  1. [1]
    D. H. Nguyen, “Minimum-rank dynamic output consensus design for heterogeneous nonlinear multi-agent systems.” IEEE Transactions on Control of Network Systems, vol. 5, no. 1, pp. 105–115. 2018.MathSciNetzbMATHGoogle Scholar
  2. [2]
    X. Wang, H. Su, L. Wang, and X. Wang, “Edge consensus on complex networks: a structural analysis,” International Journal of Control, vol. 90, no. 8, pp. 1584–1596, 2017.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Y. Han and C. Li, “Second-order consensus of discretetime multi-agent systems in directed networks with nonlinear dynamics via impulsive protocols,” Neurocomputing, vol. 286, pp. 51–57, 2018.Google Scholar
  4. [4]
    J. Liang, Z. Wang, and X. Liu, “Exponential synchronization of stochastic delayed discrete-time complex networks,” Nonlinear Dynamics, vol. 53, no. 1–2, pp. 153–165, 2008.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Z. H. Guan, Z. W. Liu, G. Feng, and Y. W. Wang, “Synchronization of complex dynamical networks with timevarying delays via impulsive distributed control,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 8, pp. 2182–2195, 2010.MathSciNetGoogle Scholar
  6. [6]
    Z. Li, J. A. Fang, Q. Miao, and G. He, “Exponential synchronization of impulsive discrete-time complex networks with time-varying delay,” Neurocomputing, vol. 157, pp. 335–343, 2015.Google Scholar
  7. [7]
    H. Li, X. Liao, G. Chen, D. J. Hill, Z. Dong, and T. Huang, “Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks,” Neural Networks, vol. 66, pp. 1–10, 2015.zbMATHGoogle Scholar
  8. [8]
    W. Sun, T. Hu, Z. Chen, S. Chen, and L. Xiao, “Impulsive synchronization of a general nonlinear coupled complex network,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4501–4507, 2011.MathSciNetzbMATHGoogle Scholar
  9. [9]
    C. Li, W. Yu, and T. Huang, “Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach,” Neural Networks, vol. 54, no. 6, pp. 85–94, 2014.zbMATHGoogle Scholar
  10. [10]
    Y. Liu, B. Z. Guo, J. H. Park, and S. M. Lee, “Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control,” IEEE transactions on neural networks and learning systems, vol. 29, no. 1, pp. 118–128, 2018.MathSciNetGoogle Scholar
  11. [11]
    Z. Tang, J. H. Park, and W. X. Zheng, “Distributed impulsive synchronization of Lur’e dynamical networks via parameter variation methods,” International Journal of Robust and Nonlinear Control, vol. 28, no. 3, pp. 1001–1015, 2018.MathSciNetzbMATHGoogle Scholar
  12. [12]
    Z. Tang, J. H. Park, Y. Wang, and J. Feng, “Distributed Impulsive Quasi-Synchronization of Lur’e Networks With Proportional Delay,” IEEE tTransactions on Cybernetics, 2018.Google Scholar
  13. [13]
    Z. Tang, J. H. Park, and J. Feng, “Novel approaches to pin cluster synchronization on complex dynamical networks in Lure forms,” Communications in Nonlinear Science and Numerical Simulation, vol. 57, pp. 422–438, 2018.MathSciNetGoogle Scholar
  14. [14]
    Y. Liu, J. H. Park, B. Z. Guo, F. Fang, and F. Zhou, “Eventtriggered dissipative synchronization for Markovian jump neural networks with general transition probabilities,” International Journal of Robust and Nonlinear Control, vol. 28, no. 13, pp. 3893–3908, 2018.MathSciNetzbMATHGoogle Scholar
  15. [15]
    T. Musa, “Complex network security analysis based on attack graph,” Neuropsychologia, vol. 12, no. 1, pp. 131–139, 2015.Google Scholar
  16. [16]
    Z. Li and G. Chen, “Global synchronization and asymptotic stability of complex dynamical networks,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 1, pp. 28–33, 2006.MathSciNetGoogle Scholar
  17. [17]
    Z. Xiao, B. Cao, J. Sun, and G. Zhou, “Culture of the stability in an eco-industrial system centered on complex network theory,” Journal of Cleaner Production, vol. 113, pp. 730–742, 2016.Google Scholar
  18. [18]
    W. J. Yuan, X. S. Luo, P. Q. Jiang, B. H. Wang, and J. Q. Fang, “Stability of a complex dynamical network model,” Physica A Statistical Mechanics and Its Applications, vol. 374, no. 1, pp. 478–482, 2007.Google Scholar
  19. [19]
    Y. Liu, J. H. Park, and F. Fang, “Global exponential stability of delayed neural networks based on a new integral inequality,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018.(in press).Google Scholar
  20. [20]
    H. Li, C. Li, T. Huang, and W. Zhang, “Fixed-time stabilization of impulsive cohen-grossberg bam neural networks,” Neural Networks, vol. 98, no. 3, pp. 203–211, 2018.Google Scholar
  21. [21]
    C. Li, S. Wu, G. G. Feng, and X. Liao, “Stabilizing effects of impulses in discrete-time delayed neural networks,” IEEE Transactions on Neural Networks, vol. 22, no. 2, pp. 323–329, 2011.Google Scholar
  22. [22]
    Z. Yang and D. Xu, “Stability analysis and design of impulsive control systems with time delay,” IEEE Transactions on Automatic Control, vol. 52, no. 8, pp. 1448–1454, 2007.MathSciNetzbMATHGoogle Scholar
  23. [23]
    N. K. Bose and Y. Shi, “Network realizability theory approach to stability of complex polynomials,” IEEE Transactions on Circuits and Systems, vol. 34, no. 2, pp. 216–218, 1987.zbMATHGoogle Scholar
  24. [24]
    D. Nesic and A. R. Teel, “Input-output stability properties of networked control systems,” IEEE Transactions on Automatic Control, vol. 49, no. 10, pp. 1650–1667, 2004.MathSciNetzbMATHGoogle Scholar
  25. [25]
    C. Li and X. Liao, “Impulsive stabilization of dlayed neural networks with and without uncertainty,” International Journal of Robust and Nonlinear Control, vol. 17, no. 16, pp. 1489–1502, 2007.MathSciNetzbMATHGoogle Scholar
  26. [26]
    X. Liu and Z. Zhang, “Uniform asymptotic stability of impulsive discrete systems with time delay,” Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 15, pp. 4941–4950, 2011.MathSciNetzbMATHGoogle Scholar
  27. [27]
    Y. Zhang, J. Sun, and G. Feng, “Impulsive control of discrete systems with time delay,” IEEE Transactions on Automatic Control, vol. 54, no. 4, pp. 830–834, 2009.MathSciNetGoogle Scholar
  28. [28]
    J. Zhou and Q. Wu, “Exponential stability of impulsive delayed linear differential equations,” IEEE Transactions on Circuits and Systems II Express Briefs, vol. 56, no. 9, pp. 744–748, 2009.Google Scholar
  29. [29]
    Y. Zhang, “Exponential stability of impulsive discrete systems with time delays,” Applied Mathematics Letters, vol. 25, no. 12, pp. 2290–2297, 2012.MathSciNetzbMATHGoogle Scholar
  30. [30]
    J. Lu, D. W. Ho, and J. Cao, “A unified synchronization criterion for impulsive dynamical networks,” Automatica, vol. 46, no. 7, pp. 1215–1221, 2010.MathSciNetzbMATHGoogle Scholar
  31. [31]
    P. Cheng, F. Deng, and F. Yao, “Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects,” Nonlinear Analysis Hybrid Systems, vol. 30, no. 4, pp. 106–117, 2018.MathSciNetzbMATHGoogle Scholar
  32. [32]
    X. Li and S. Song, “Stabilization of delay systems:delaydependent impulsive control,” IEEE Transactions on Automatic Control, vol. 62, no. 1, pp. 406–411, 2016.Google Scholar
  33. [33]
    X. Li, J. Shen, H. Akca, and R. Rakkiyappan, “Comparison principle for impulsive functionaldifferential equations with infinite delays and applications,” Communications in Nonlinear Science and Numerical Simulation, vol. 57, pp. 309–321, 2018.MathSciNetGoogle Scholar
  34. [34]
    Z. G. Li, C. Y. Wen, and Y. C. Soh, “Analysis and design of impulsive control systems,” IEEE Transactions on Automatic Control, vol. 46, no. 6, pp. 894–897, 2001.MathSciNetzbMATHGoogle Scholar
  35. [35]
    Z. Lu, X. Chi, and L. Chen, “Impulsive control strategiesin biological control of pesticide,” Theoretical Population Biology, vol. 64, no. 1, pp. 39–47, 2003.zbMATHGoogle Scholar
  36. [36]
    Y. Li, X. Liao, C. Li, T. Huang, and D. Yang, “Impulsive synchronization and parameter mismatch of the threevariable autocatalator model,” Physics Letters A, vol. 366, no. 1–2, pp. 52–60, 2007.Google Scholar
  37. [37]
    B. M. Miller and E. Y. Rubinovich, Impulsive Control in Continuous and Discrete-continuous Systems, Springer Science and Business Media, 2012.zbMATHGoogle Scholar
  38. [38]
    J. Sun, Y. Zhang, and Q. Wu, “Less conservative conditions for asymptotic stability of impulsive control systems,” IEEE Transactions on automatic control, vol. 48, no. 5, pp. 829–831, 2003.MathSciNetzbMATHGoogle Scholar
  39. [39]
    M. S. Ali and J. Yogambigai, “Exponential stability of semi-markovian switching complex dynamical networks with mixed time varying delays and impulse control,” Neural Processing Letters, vol. 46, pp. 1–21, 2016.Google Scholar
  40. [40]
    X. Li, W. H. Chen, W. X. Zheng, and Q. G. Wang, “Instability and unboundedness analysis for impulsive differential systems with applications to lurie control systems,” International Journal of Control Automation and Systems, vol. 16, no. 4, pp. 1521–1531, 2018.Google Scholar
  41. [41]
    C. Li, Y. Zhou, H. Wang, and T. Huang, “Stability of nonlinear systems with variable-time impulses: b-equivalence method,” International Journal of Control Automation and Systems, vol. 15, no. 5, pp. 2072–2079, 2017.Google Scholar
  42. [42]
    J. Tan, C. Li, and T. Huang, “Comparison System Method for a class of Stochastic Systems with Variable-time Impulses,” International Journal of Control Automation and Systems, vol. 16, no. 2, pp. 702–708, 2018.Google Scholar
  43. [43]
    X. Tan, B. Hu, Z. H. Guan, R. Q. Liao, J. W. Xiao, and Y. Huang, “Stability of hybrid impulsive and switching stochastic systems with time-delay,” International Journal of Control Automation and Systems, vol. 16, no. 4, pp. 1532–1540, 2018.Google Scholar
  44. [44]
    M. J. Hu, Y. W. Wang, and J. W. Xiao, “Positive observer design for linear impulsive positive systems with interval uncertainties and time delay,” International Journal of Control Automation and Systems, vol. 15, no. 3, pp. 1032–1039, 2017.Google Scholar
  45. [45]
    T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design, Springer Science and Business Media, 2001.Google Scholar
  46. [46]
    L. Li, C. Li, and H. Li, “An analysis and design for timevarying structures dynamical networks via state constraint impulsive control,” International Journal of Control, pp. 1–9, 2018.Google Scholar
  47. [47]
    L. Li, C. Li, and H. Li, “Fully state constraint impulsive control for non-autonomous delayed nonlinear dynamic systems,” Nonlinear Analysis: Hybrid Systems, vol. 29, pp. 383–394, 2018.MathSciNetzbMATHGoogle Scholar
  48. [48]
    Z. Li, J. A. Fang, T. Huang, Q. Miao, and H. Wang, “Impulsive synchronization of discrete-time networked oscillators with partial input saturation,” Information Sciences, vol. 422, no. 3, pp. 531–541, 2018.Google Scholar
  49. [49]
    Z. H. Guan, Z. W. Liu, G. Feng, and Y. W. Wang, “Synchronization of complex dynamical networks with timevarying delays via impulsive distributed control,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 8, pp. 2182–2195, 2010.MathSciNetGoogle Scholar
  50. [50]
    J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays,” IEEE Transactions on Neural Networks, vol. 13, no. 2, pp. 457–463, 2002.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.College of Electronic and Information EngineeringSouthwest universityChongqingChina
  2. 2.National & Local Joint Engineering Laboratory of Intelligent Transmission and Control TechnologyChongqingChina
  3. 3.Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic Information EngineeringSouthwest UniversityChongqingChina
  4. 4.Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, and also with School of Mathematics and StatisticsChongqing Three Gorges UniversityChongqingChina

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