Skip to main content
SpringerLink
Log in

Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

This paper concerns the stabilization of switched dynamical networks with logarithmic quantization couplings in a settling time. The switching sequence is constrained by hybrid dwell time. Controller is designed by using limited information. Due to the quantization and switching, traditional finite-time analysis methods cannot be utilized directly. By designing multiple Lyapunov functions and constructing comparison systems, a general criterion formulated by matrix inequalities is first given. Then specific conditions in terms of linear matrix inequalities are established by partitioning the dwell time and using convex combination technique. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are given to verify the effectiveness of the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Duan Z, Wang J, Chen G, et al. Stability analysis and decentralized control of a class of complex dynamical networks. Automatica, 2008, 44: 1028–1035

    Article  MathSciNet  MATH  Google Scholar 

  2. Lu J, Ho DWC, Wu L. Exponential stabilization of switched stochastic dynamical networks. Nonlinearity, 2009, 22: 889–911

    Article  MathSciNet  MATH  Google Scholar 

  3. Wang Y, Fan Y, Wang Q, et al. Stabilization and synchronization of complex dynamical networks with different dynamics of nodes via decentralized controllers. IEEE Trans Circuits Syst I, 2012, 59: 1786–1795

    Article  MathSciNet  Google Scholar 

  4. Yu J, Sun G. Robust stabilization of stochastic Markovian jumping dynamical networks with mixed delays. Neurocomputing, 2012, 86: 107–115

    Article  Google Scholar 

  5. Chen W H, Lu X M, Wei X Z. Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks. IEEE Trans Neural Netw Learning Syst, 2015, 26: 734–748

    Article  MathSciNet  Google Scholar 

  6. Zhang G, Shen Y. Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans Neural Netw Learning Syst, 2015, 26: 1431–1441

    Article  MathSciNet  Google Scholar 

  7. Liu Y, Cao J, Sun L, et al. Sampled-data state feedback stabilization of boolean control networks. Neural Comput, 2016, 28: 778–799

    Article  Google Scholar 

  8. Yang X, Ho D W C, Lu J, et al. Finite-time cluster synchronization of T-S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst, 2015, 23: 2302–2316

    Article  Google Scholar 

  9. Fan H W, Wang Y F, Chen M J, et al. Chaos synchronization with dual-channel time-delayed couplings. Sci China Tech Sci, 2016, 59: 428–435

    Article  Google Scholar 

  10. Rakkiyappan R, Sasirekha R. Asymptotic synchronization of continuous/ discrete complex dynamical networks by optimal partitioning method. Complexity, 2015, 21: 193–210

    Article  MathSciNet  Google Scholar 

  11. Han Q K, Sun X Y, Yang X G, et al. External synchronization of two dynamical systems with uncertain parameters. Sci China Tech Sci, 2010, 53: 731–740

    Article  MATH  Google Scholar 

  12. Li T T. From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems. Sci China Math, 2016, 59: 1–18

    MathSciNet  MATH  Google Scholar 

  13. Sorrentino F, Pecora L M, Hagerstrom A M, et al. Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci Adv, 2016, 2: e1501737

    Article  Google Scholar 

  14. Yang X, Lu J. Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Automat Contr, 2016, 61: 2256–2261

    Article  MathSciNet  MATH  Google Scholar 

  15. Li H, Liao X, Chen G, et al. Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Netw, 2015, 66: 1–10

    Article  Google Scholar 

  16. Huang N, Duan Z S, Zhao Y. Distributed consensus for multiple Euler-Lagrange systems: An event-triggered approach. Sci China Tech Sci, 2016, 59: 33–44

    Article  Google Scholar 

  17. Ceragioli F, De Persis C, Frasca P. Discontinuities and hysteresis in quantized average consensus. Automatica, 2011, 47: 1916–1928

    Article  MathSciNet  MATH  Google Scholar 

  18. Li L, Ho D W C, Lu J. A unified approach to practical consensus with quantized data and time delay. IEEE Trans Circuits Syst I, 2013, 60: 2668–2678

    Article  MathSciNet  Google Scholar 

  19. Liu S, Li T, Xie L, et al. Continuous-time and sampled-data-based average consensus with logarithmic quantizers. Automatica, 2013, 49: 3329–3336

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu M, Cao X, Zhang S, et al. Sliding mode control of quantized systems against bounded disturbances. Inf Sci, 2014, 274: 261–272

    Article  MathSciNet  MATH  Google Scholar 

  21. Shi P, Liu M, Zhang L. Fault-tolerant sliding-mode-observer synthesis of Markovian jump systems using quantized measurements. IEEE Trans Ind Electron, 2015, 62: 5910–5918

    Article  Google Scholar 

  22. Xiao N, Xie L, Fu M. Stabilization of Markov jump linear systems using quantized state feedback. Automatica, 2010, 46: 1696–1702

    Article  MathSciNet  MATH  Google Scholar 

  23. Liberzon D. Finite data-rate feedback stabilization of switched and hybrid linear systems. Automatica, 2014, 50: 409–420

    Article  MathSciNet  MATH  Google Scholar 

  24. Cao J D, Rakkiyappan R, Maheswari K, et al. Exponential H ∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Sci China Tech Sci, 2016, 59: 387–402

    Article  Google Scholar 

  25. Hetel L, Daafouz J, Iung C. Stabilization of arbitrary switched linear systems with unknown time-varying delays. IEEE Trans Automat Contr, 2006, 51: 1668–1674

    Article  MathSciNet  MATH  Google Scholar 

  26. Daafouz J, Riedinger P, Iung C. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach. IEEE Trans Automat Contr, 2002, 47: 1883–1887

    Article  MathSciNet  MATH  Google Scholar 

  27. Xiang W, Xiao J. Stabilization of switched continuous-time systems with all modes unstable via dwell time switching. Automatica, 2014, 50: 940–945

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhao X, Yin S, Li H, et al. Switching stabilization for a class of slowly switched systems. IEEE Trans Automat Contr, 2015, 60: 221–226

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang Y W, Yang M, Wang H O, et al. Robust stabilization of complex switched networks with parametric uncertainties and delays via impulsive control. IEEE Trans Circuits Syst I, 2009, 56: 2100–2108

    Article  MathSciNet  Google Scholar 

  30. Yang X, Song Q, Liu Y, et al. Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing, 2015, 152: 19–26

    Article  Google Scholar 

  31. Oza H B, Orlov Y V, Spurgeon S K. Continuous uniform finite time stabilization of planar controllable systems. SIAM J Control Optim, 2015, 53: 1154–1181

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu K X, Wu L L, Lü J H, et al. Finite-time adaptive consensus of a class of multi-agent systems. Sci China Tech Sci, 2016, 59: 22–32

    Article  Google Scholar 

  33. Bao H, Cao J. Finite-time generalized synchronization of nonidentical delayed chaotic systems. Nonlinear Anal Model Control, 2016, 21: 306–324

    MathSciNet  Google Scholar 

  34. Li S, Sun H, Yang J, et al. Continuous finite-time output regulation for disturbed systems under mismatching condition. IEEE Trans Automat Contr, 2015, 60: 277–282

    Article  MathSciNet  MATH  Google Scholar 

  35. Cao J, Li R. Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci, 2017, 60: 032201

    Article  Google Scholar 

  36. Polyakov A, Efimov D, Perruquetti W. Finite-time and fixed-time stabilization: Implicit Lyapunov function approach. Automatica, 2015, 51: 332–340

    Article  MathSciNet  MATH  Google Scholar 

  37. Orlov Y. Finite time stability and robust control synthesis of uncertain switched systems. SIAM J Control Optim, 2004, 43: 1253–1271

    Article  MathSciNet  MATH  Google Scholar 

  38. Cai M, Xiang Z, Guo J. Adaptive finite-time control for a class of switched nonlinear systems using multiple Lyapunov functions. Int J Syst Sci, 2017, 48: 324–336

    Article  MathSciNet  MATH  Google Scholar 

  39. Tang Y. Terminal sliding mode control for rigid robots. Automatica, 1998, 34: 51–56

    Article  MathSciNet  MATH  Google Scholar 

  40. Lu J, Ho D W C, Cao J. A unified synchronization criterion for impulsive dynamical networks. Automatica, 2010, 46: 1215–1221

    Article  MathSciNet  MATH  Google Scholar 

  41. Mastellone S, Dorato P, Abdallah C T. Finite-time stability of discretetime nonlinear systems: Analysis and design. In: 43rd IEEE Conference on Decision and Control. Paradise Island, 2004. 2572–2577

    Google Scholar 

  42. Horn R, Johnson C. Matrix Analysis. Cambridge: Cambridge University Press, 1990

    MATH  Google Scholar 

  43. Wang Y, Xie L, de Souza C E. Robust control of a class of uncertain nonlinear systems. Syst Control Lett, 1992, 19: 139–149

    Article  MathSciNet  MATH  Google Scholar 

  44. Boyd S, El Ghaoui L, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    XinSong Yang

  2. School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, China

    JinDe Cao

  3. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Chen Xu & JianWen Feng

Authors
  1. XinSong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JinDe Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chen Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. JianWen Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to XinSong Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Cao, J., Xu, C. et al. Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci. China Technol. Sci. 61, 299–308 (2018). https://doi.org/10.1007/s11431-016-9054-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-016-9054-y

Keywords

Search

Navigation