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Improved Stabilization Results for Markovian Switching CVNNs with Partly Unknown Transition Rates

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Abstract

In this paper, stochastic stability and stabilization problems are investigated for the Markovian switching complex-valued neural networks with mixed delays, where the transition rates (TRs) of the Markov chain are partly unknown, which might reflect more the realistic dynamical behaviors of the neural networks. On the basis of the Lyapunov stability theory and the stochastic analysis method as well as the properties of the TR matrix, several mode-dependent criteria are derived to guarantee the considered complex-valued network to be globally asymptotically stable in mean-square sense. Then, by proposing an appropriate mode-dependent controller, stabilization conditions in terms of matrix inequalities are derived to guarantee the closed-loop system to be stochastically mean-square stable. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical results.

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References

  1. Hu S, Wang J (2002) Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks. IEEE Trans Autom Control 47(5):802–807

    Article  MathSciNet  Google Scholar 

  2. Wang Z, Zhang H, Yu W (2009) Robust stability of Cohen–Grossberg neural networks via state transmission matrix. IEEE Trans Neural Netw 20(1):169–174

    Article  Google Scholar 

  3. Ohtani N, Nagai N, Suzuki M, Miki N (1991) Formulation of quantum effects by using complex-valued equivalent circuit. Electron Commun Jpn II Electron 74(7):11–19

    Article  Google Scholar 

  4. Gronwald F, Nitsch J, Tkachenko S (2012) On equivalent circuit representations for radiating systems by means of complex-valued network elements. In: 2012 international conference on electromagnetics in advanced applications, Cape Town, South Africa, September 02–07, pp 710–713

  5. Chen X, Cao J, Park JH, Zong G, Qiu J (2018) Finite-time complex function synchronization of multiple complex-variable chaotic systems with network transmission and combination mode. J Vib Control 24(22):5461–5471

    Article  MathSciNet  Google Scholar 

  6. Nitta T (2003) Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Netw 16(8):1101–1105

    Article  MathSciNet  Google Scholar 

  7. Hirose A (2010) Recent progress in applications of complex-valued neural networks. In: Proceeding of the 10th international conference on artifical intelligence and soft computing, Zakopane, Poland, Jun 13–17, pp 42–46

  8. Savitha R, Suresh S, Sundararajan N (2012) Meta-cognitive learning in fully complex-valued radial basis function network. Neural Comput 24(5):1297–1328

    Article  MathSciNet  Google Scholar 

  9. Goh SL, Chen M, Popović DH, Obradovic D, Mandic DP (2006) Complex-valued forecasting of wind profile. Renew Energy 31(11):1733–1750

    Article  Google Scholar 

  10. Li Q, Liang J, Gong W (2019) Stability and synchronization for impulsive Markovian switching CVNNs: matrix measure approach. Commun Nonlinear Sci Numer Simul 77:126–140

    Article  MathSciNet  Google Scholar 

  11. Gong W, Liang J, Cao J (2015) Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays. Neural Netw 70:81–89

    Article  Google Scholar 

  12. Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 3(6):853–865

    Article  Google Scholar 

  13. Velmurugan G, Rakkiyappan R, Lakshmanan S (2015) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42(3):517–540

    Article  Google Scholar 

  14. Fang T, Sun J (2014) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25(9):1709–1713

    Article  Google Scholar 

  15. Zhang L, Yang X, Xu C, Feng J (2017) Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control. Appl Math Comput 306:22–30

    MathSciNet  MATH  Google Scholar 

  16. Gao H, Chen T (2007) New results on stability of discrete-time systems with time-varying state delay. IEEE Trans Autom Control 52(2):328–334

    Article  MathSciNet  Google Scholar 

  17. Boukas EK, Liu ZK (2002) Deterministic and stochastic time-delay systems. Birkhäuser, Basel

    Book  Google Scholar 

  18. Liang J, Wang Z, Liu Y, Liu X (2008) Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans Syst Man Cybern B-Cybern 38(4):1073–1083

    Article  Google Scholar 

  19. Zhou C, Zhang W, Yang X, Xu C, Feng J (2017) Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett 46(1):271–291

    Article  Google Scholar 

  20. Song Q, Shu H, Liu Y, Alsaadi FE (2017) Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 244:33–41

    Article  Google Scholar 

  21. Chen X, Song Q, Liu Y, Zhao Z (2014) Global \(\mu \)-stability of impulsive complex-valued neural networks with leakage delay and mixed delays. Abstr Appl Anal 2014 Art. No. 397532

  22. Liu Q, Wang Z, He X, Zhou D (2019) Event-based distributed filtering over Markovian switching topologies. IEEE Trans Autom Control 64(4):1595–1602

    Article  MathSciNet  Google Scholar 

  23. Wang Z, Liu Y, Liu X (2010) Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans Autom Control 55(7):1656–1662

    Article  MathSciNet  Google Scholar 

  24. Wu Y, Cao J, Li Q, Alsaedi A, Alsaadi FE (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139

    Article  Google Scholar 

  25. Yang X, Song Q, Cao J, Lu J (2018) Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst 30(3):951–958

    Article  MathSciNet  Google Scholar 

  26. Zhu E, Yin G, Yuan Q (2016) Stability in distribution of stochastic delay recurrent neural networks with Markovian switching. Neural Comput Appl 27(7):2141–2151

    Article  Google Scholar 

  27. Li D, Ma C (2014) Attractor and stochastic boundedness for stochastic infinite delay neural networks with Markovian switching. Neural Process Lett 40(2):127–142

    Article  Google Scholar 

  28. Raja R, Raja UK, Samidurai R, Leelamani A (2013) Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses. J Frankl Inst 350(10):3217–3247

    Article  MathSciNet  Google Scholar 

  29. Liang J, Lam J, Wang Z (2009) State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates. Phys Lett A 373(47):4328–4337

    Article  MathSciNet  Google Scholar 

  30. Xiong J, Lam J (2009) Robust \(H_2\) control of Markovian jump systems with uncertain switching probabilities. Int J Syst Sci 40(3):255–265

    Article  Google Scholar 

  31. Li Q, Liang J (2020) Dissipativity of the stochastic Markovian switching CVNNs with randomly occurring uncertainties and general uncertain transition rates. Int J Syst Sci 51(6):1102–1118

    Article  MathSciNet  Google Scholar 

  32. Zhang L, Boukas EK (2009) Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(2):463–468

    Article  MathSciNet  Google Scholar 

  33. Zhang L, Boukas EK (2009) \(H_{\infty }\) control for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Int J Robust Nonlinear Control 19(8):868–883

    Article  MathSciNet  Google Scholar 

  34. Kao Y, Xie J, Zhang L, Karimi HR (2015) A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates. Nonlinear Anal-Hybrid Syst 17:70–80

    Article  MathSciNet  Google Scholar 

  35. 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 121:254–264

    Article  Google Scholar 

  36. Dynkin EB (1965) Markov processes. Springer, Heidelberg

    Book  Google Scholar 

  37. Zhang L, Lam J (2010) Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions. IEEE Trans Autom Control 55(7):1695–1701

    Article  MathSciNet  Google Scholar 

  38. Gahinet P, Nemirovskii A, Laub AJ, Chilali M (1994) The LMI control toolbox. In: Proceedings of the 33rd IEEE conference on decision and control, Lake Buena Vista, FL, USA, December 14–16, pp 2038–2041

  39. Zou L, Wang Z, Han Q-L, Zhou D (2019) Moving horizon estimation for networked time-delay systems under Round-Robin protocol. IEEE Trans Autom Control 64(12):5191–5198

    Article  MathSciNet  Google Scholar 

  40. Wang F, Wang Z, Liang J, Liu X (2020) Recursive distributed filtering for two-dimensional shift-varying systems over sensor networks under stochastic communication protocols. Automatica 115 Art. No. 108865

  41. Liu J, Zhang Y, Yu Y, Sun C (2019) Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications. IEEE Trans Syst Man Cybern-Syst 49(11):2221–2229

    Article  Google Scholar 

  42. Liu J, Zhang Y, Yu Y, Sun C (2019) Fixed-time leader-follower consensus of networked nonlinear systems via event/self-triggered control. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2019.2957069

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Key Research and Development Program of China under Grant 2018AAA0100202, in part by the National Natural Science Foundation of China under Grant 61673110, in part by the Fundamental Research Funds for the Central Universities under Grant 2242020K40236, and in part by the Scientific Research Foundation of Graduate School of Southeast University under Grant YBPY1870.

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  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Qiang Li & Jinling Liang

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  1. Qiang Li
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  2. Jinling Liang
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Correspondence to Jinling Liang.

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Li, Q., Liang, J. Improved Stabilization Results for Markovian Switching CVNNs with Partly Unknown Transition Rates. Neural Process Lett 52, 1189–1205 (2020). https://doi.org/10.1007/s11063-020-10299-4

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