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Synchronization of Discrete-Time Switched 2-D Systems with Markovian Topology via Fault Quantized Output Control

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Abstract

This paper considers the global exponential synchronization almost surely (GES a.s.) in an array of two-dimensional (2-D) discrete-time systems with Markovian jump topology. Considering the fact that external disturbances are inevitable and communication resources are limited, mode-dependent quantized output control with actuator fault (AF) is designed. Sufficient conditions formulated by linear matrix inequalities (LMIs) are given to ensure the GES a.s. Control gains of the controller without AF is designed by solving the LMIs. It is shown that the stationary distribution of the transition probability of the Markov chain plays an important role in our study, which makes it possible that some of the modes are not controlled. Numerical examples are given to illustrate the effectiveness of theoretical analysis.

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References

  1. Yang X, Cao J et al (2013) Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM J Control Optim 51(5):3486–3510

    MathSciNet  MATH  Google Scholar 

  2. Yang X, Ho DWC (2016) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Syst Man Cybern 46(12):3377–3387

    Google Scholar 

  3. Yang X, Cao J et al (2012) Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Trans Neural Netw Learn Syst 23(1):60–71

    Google Scholar 

  4. Yang X, Ho DWC et al (2015) Finite-time cluster synchronization of T-S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst 23(6):2302–2316

    Google Scholar 

  5. Tang R, Yang X et al (2019) Finite-time synchronization of nonidentical BAM discontinuous fuzzy neural networks with delays and impulsive effects via non-chattering quantized control. Commun Nonlinear Sci Numer Simul 78:104893

    MathSciNet  MATH  Google Scholar 

  6. Yang X, Feng Y et al (2018) Synchronization of coupled neural networks with infinite-time distributed delays via quantized intermittent pinning control. Nonlinear Dyn 94(3):2289–2303

    MATH  Google Scholar 

  7. Liu Y, Wang Z et al (2009) Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Trans Neural Netw 20(7):1102–1116

    Google Scholar 

  8. Yang X, Feng Z et al (2017) Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw 85:157–164

    MATH  Google Scholar 

  9. Wu L, Feng Z et al (2013) Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays. IEEE Trans Neural Netw 24(12):1957–1972

    Google Scholar 

  10. Roesser R (1975) A discrete state-space model for linear image processing. IEEE Trans Autom Control 20(1):1–10

    MathSciNet  MATH  Google Scholar 

  11. Du C, Xie L et al (2001) \(H_{\infty }\) control and robust stabilization of two-dimensional systems in Roesser models. Automatica 37(2):205–211

    MathSciNet  MATH  Google Scholar 

  12. De Souza CE et al (2013) Gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems in the Roesser model. Automatica 49(1):101–110

    MathSciNet  MATH  Google Scholar 

  13. Wua L, Yang R et al (2015) Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings. Automatica 59:206–215

    MathSciNet  Google Scholar 

  14. Ahn CK, Wu L et al (2016) Stochastic stability analysis for 2-D Roesser systems with multiplicative noise. Automatica 69(69):356–363

    MathSciNet  MATH  Google Scholar 

  15. Liang J, Wang Z et al (2012) Robust synchronization for 2-D discrete-time coupled dynamical networks. IEEE Trans Neural Netw 23(6):942–953

    Google Scholar 

  16. Li X, Gao H (2013) Robust finite frequency \(H_{\infty }\) filtering for uncertain 2-D systems: the FM model case. Automatica 49(8):2446–2452

    MathSciNet  MATH  Google Scholar 

  17. Ahn CK, Shi P et al (2015) Two-dimensional dissipative control and filtering for Roesser model. IEEE Trans Autom Control 60(7):1745–1759

    MathSciNet  MATH  Google Scholar 

  18. Li D, Liang J et al (2019) \(H_{\infty }\) state estimation for two-dimensional systems with randomly occurring uncertainties and Round-Robin protocol. Neurocomputing 349:248–260

    Google Scholar 

  19. Li D, Liang J et al (2019) Dissipative networked filtering for two-dimensional systems with randomly occurring uncertainties and redundant channels. Neurocomputing 369:1–10

    Google Scholar 

  20. Fei Z, Shi S et al (2018) Quasi-time-dependent output control for discrete-time switched system with mode-dependent average dwell time. IEEE Trans Autom Control 63(8):2647–2653

    MathSciNet  MATH  Google Scholar 

  21. Yang X, Cao J et al (2018) Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci 61(2):299–308

    Google Scholar 

  22. Yang X, Huang C et al (2011) Synchronization of switched neural networks with mixed delays via impulsive control. Chaos Solitons Fractals 44(10):817–826

    MathSciNet  MATH  Google Scholar 

  23. Huang M, Dey S et al (2010) Stochastic consensus over noisy networks with Markovian and arbitrary switches. Automatica 46(10):1571–1583

    MathSciNet  MATH  Google Scholar 

  24. Kori H, Kuramoto Y (2001) Slow switching in globally coupled oscillators: robustness and occurrence through delayed coupling. Phys Rev E 63(4):046214

    Google Scholar 

  25. Johansson KH, Rantzer A et al (1999) Fast switches in relay feedback systems. Automatica 35(4):539–552

    MATH  Google Scholar 

  26. Zhao X, Zhang L et al (2012) Stability of switched positive linear systems with average dwell time switching. Automatica 48(6):1132–1137

    MathSciNet  MATH  Google Scholar 

  27. Yang X, Liu Y et al (2020) Synchronization of coupled time-delay neural networks with mode-dependent average dwell time switching. IEEE Trans Neural Netw Learn Syst 31(12):5483–5496

    MathSciNet  Google Scholar 

  28. Yang X, Li X et al (2020) Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control. IEEE Trans Cybern 50(9):4043–4052

    Google Scholar 

  29. Yang X, Song Q et al (2019) Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst 3(3):951–958

    MathSciNet  Google Scholar 

  30. Mao X (2002) Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans Autom Control 47(10):1604–1612

    MathSciNet  MATH  Google Scholar 

  31. Yue D, Han Q (2005) Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching. IEEE Trans Autom Control 50(2):217–222

    MathSciNet  MATH  Google Scholar 

  32. Wan X, Yang X et al (2019) Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller. Neural Netw 118:321–331

    MATH  Google Scholar 

  33. Yang X, Cao J et al (2013) Synchronization of randomly coupled neural networks with Markovian jumping and time-delay. IEEE Trans Circuits Syst I 60(2):363–376

    MathSciNet  MATH  Google Scholar 

  34. Chandrasekar A, Rakkiyappan R et al (2014) Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control. Neurocomputing 133:385–398

    Google Scholar 

  35. Zhou C, Zhang W et al (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46:271–291

    Google Scholar 

  36. Huang Y, Ren S (2018) Passivity and passivity-based synchronization of switched coupled reaction-diffusion neural networks with state and spatial diffusion couplings. Neural Process Lett 47:347–363

    Google Scholar 

  37. Cao Y, Wen S et al (2017) New criteria on exponential lag synchronization of switched neural networks with time-varying delays. Neural Process Lett 46:451–466

    Google Scholar 

  38. Xiong X, Tang R et al (2019) Finite-time synchronization of memristive neural networks with proportional delay. Neural Process Lett 50:1139–1152

    Google Scholar 

  39. Wu L, Su X et al (2014) Output feedback control of Markovian jump repeated scalar nonlinear systems. IEEE Trans Autom Control 59(1):199–204

    MathSciNet  MATH  Google Scholar 

  40. Fu M, Xie L (2005) The sector bound approach to quantized feedback control. IEEE Trans Autom Control 50(11):1698–1711

    MathSciNet  MATH  Google Scholar 

  41. Xiong X, Yang X et al (2020) Finite-time control for a class of hybrid systems via quantized intermittent control. Sci China Inf Sci 63(9):192201

    MathSciNet  Google Scholar 

  42. Tang R, Yang X et al (2019) Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers. Neural Netw 113:79–90

    MATH  Google Scholar 

  43. Kostarigka AK, Rovithakis GA (2012) Adaptive dynamic output feedback neural network control of uncertain MIMO nonlinear systems with prescribed performance. IEEE Trans Neural Netw 23(1):138–149

    Google Scholar 

  44. Yang X, Cheng Z et al (2019) Exponential synchronization of coupled neutral-type neural networks with mixed delays via quantized output control. J Frankl Inst 356(15):8138–8153

    MathSciNet  MATH  Google Scholar 

  45. Chen M, Shi P et al (2016) Adaptive neural fault-tolerant control of a 3-dof model helicopter system. IEEE Trans Syst Man Cybern 46(2):260–270

    Google Scholar 

  46. Yang X, Wan X et al (2020) Synchronization of switched discrete-time neural networks via quantized output control with actuator fault. Syst IEEE Trans Neural Netw Learn. https://doi.org/10.1109/TNNLS.2020.3017171

    Article  Google Scholar 

  47. Li Z, Li C et al (2019) A fault-tolerant method for motion planning of industrial redundant manipulator. IEEE Trans Ind Inform 16(12):7469–7478

    Google Scholar 

  48. Wu L, Yao X et al (2012) Generalized \(H_2\) fault detection for two-dimensional Markovian jump systems. Automatica 48:1741–1750

    MathSciNet  MATH  Google Scholar 

  49. Talebi HA, Khorasani K et al (2009) A recurrent neural-network-based sensor and actuator fault detection and isolation for nonlinear systems with application to the satellite’s attitude control subsystem. IEEE Trans Neural Netw 20(1):45–60

  50. Parker LE (1998) Alliance: an architecture for fault tolerant multirobot cooperation. Int Conf Robot Autom 14(2):220–240

    Google Scholar 

  51. Mecrow BC, Jack AG et al (1995) Fault tolerant permanent magnet machine drives. Int Electr Mach Drives Conf 143(6):437–442

    Google Scholar 

  52. Welchko BA, Lipo TA et al (2003) Fault tolerant three-phase AC motor drive topologies: a comparison of features, cost, and limitations. Int Electr Mach Drives Conf 19(4):1108–1116

    Google Scholar 

  53. Boskovic JD, Mehra RK (2010) A decentralized fault-tolerant control system for accommodation of failures in higher-order flflight control actuators. IEEE Trans Control Syst Technol 18(5):1103–1115

    Google Scholar 

  54. Wang Y, Xie L et al (1992) Robust control of a class of uncertain nonlinear systems. Syst Control Lett 19(2):139–149

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant No. 61673078, the Basic and Frontier Research Project of Chongqing under Grant No. cstc2018jcyjAX0369, Special Funds for Basic Research in Local Undergraduate Universities (Part) of Yunnan Province of China under Grant No. 2018FH001-113, and the Chongqing Graduate Research Innovation Project under Grant No. CYS19296.

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Authors and Affiliations

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

    Xue Qin & Yi Zou

  2. Department of Mathematics, Guilin University of Technology, Guilin, 541000, People’s Republic of China

    Lei Shi

  3. School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China

    Zhengwen Tu

  4. College of Intelligent Manufacturing, Zhanjiang University of Science and Technology, Zhanjiang, 524000, China

    Xiaolin Xiong

  5. College of Electronics and Information Engineering, Sichuan University, Chengdu, 610065, China

    Xinsong Yang

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  1. Xue Qin
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Correspondence to Xinsong Yang.

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Qin, X., Shi, L., Zou, Y. et al. Synchronization of Discrete-Time Switched 2-D Systems with Markovian Topology via Fault Quantized Output Control. Neural Process Lett 54, 165–180 (2022). https://doi.org/10.1007/s11063-021-10626-3

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  • DOI: https://doi.org/10.1007/s11063-021-10626-3

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