Exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay

Abstract

This paper discusses the problem of exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay. Based on non-convolution type multiple Lyapunov functions and stochastic analysis method, we obtain the conditions which are independent to any decay rate of the exponential stability for uncertain transition probabilities neutral stochastic systems with time-varying delay. Finally, two examples are presented to illustrate the effectiveness and potential of the proposed results.

Keywords

Exponential stability neutral stochastic systems time-varying delay general transition probabilities

Get full access to this article

View all access options for this article.

References

Boukas

(2005) Stochastic Switching Systems: Analysis and Design. Boston: Birkhauser.

Chen

Shi

(2016) Exponential stability for neutral stochastic Markov systems with time-varying delay and its applications. IEEE Transactions on Cybernetics 6: 1350–1362.

Chen

Zheng

(2016) Stability analysis and control for switched stochastic delayed systems. International Journal of Robust and Nonlinear Control 2: 303–328.

Chen

Zheng

Xue

(2010) A new result on stability analysis for stochastic neutral systems. Automatica 12: 2100–2104.

Cheng

Park

Karimi

et al . (2017) Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays. Information Sciences 399: 219–238.

Deng

Mao

Wan

(2013) A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems. Applied Mathematics Computation 15: 132–143.

Gao

Liu

(2013) On exponential stabilization for a class of neutral-type systems with parameter uncertainties: An integral sliding mode approach. Applied Mathematics Computation 23: 1044–1055.

Guo

Wang

(2013) Stability of Markovian jump systems with generally uncertain transition rates. Journal of the Franklin Institute 350: 2826–2836.

Hale

Meyer

(1967) A class of functional equations of neutral type. Memoirs of the American Mathematical Society 76: 1–65.

10.

Huang

Long

(2015) Stabilization for a class of Markovian jump linear systems with linear fractional uncertainties. International Journal of Innovative Computing Information and Control 1: 295–307.

11.

Huang

Mao

(2009) Delay-dependent exponential stability of neutral stochastic delay systems. IEEE Transactions on Automatic Control 1: 147–152.

12.

Kao

Shi

Xie

et al . (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Networks 63: 18–30.

13.

Kwon

Park

Lee

et al . (2013) Stability for neural networks with time-varying delays via some new approaches. IEEE Transactions Neural Networks and Learning Systems 2: 181–193.

14.

Kwon

Park

et al . (2012) New delay-partitioning approaches to stability criteria for uncertain neutral systems with time varying delays. Journal of The Franklin Institute 349: 2799–2823.

15.

Lee

Park

Kwon

et al . (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Networks 1: 99–108.

16.

Cao

(2016) Finite-time stability analysis for Markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Transactions on Neural Networks and Learning Systems : 1–12.

17.

(2010) Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Applied Mathematics Computation 12: 4370–4384.

18.

Lian

Feng

Shi

(2013) Robust filtering for a class of uncertain stochastic hybrid neutral systems with time-varying delay. International Journal of Adaptive Control and Signal Processing 27: 447–540.

19.

Liu

Xie

(2009) Exponential stability of switched stochastic delay systems with non-linear uncertainties. International Journal of Systems Science 40: 637–648.

20.

Mao

(1999) Asymptotic properties of neutral stochastic differential delay equations. Stochastics Reports 3–4: 273–295.

21.

Mao

(2008) Stochastic Differential Equations and Applications, Seconded. Chichester: Horwood Publishing.

22.

Mao

Shen

Yuan

(2008) Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching. Stochasitic Processes and their Application 8: 1385–1406.

23.

Mao

Yuan

(2006) Stochastic Differential Equations with Markovian Switching. London: Imperial College Press.

24.

Niculescu

(2001) Delay Effects on Stability: A Robust Control Approach. Berlin: Spinger.

25.

Pavlovic

Jankovic

(2013) The Razumikhin approach on general decay stability for neutral stochastic functional differential equations. Journal of The Franklin Institute 350: 2124–2145.

26.

Shen

Park

(2016) A separated approach to control of Markov jump nonlinear systems with general transition probabilites. IEEE Transactions on Cybernetics 49: 2010–2018.

27.

Shi

Xia

Liu

et al . (2006) On designing of sliding-mode control for stochastic jump systems. IEEE Transactions on Automatic Control 1: 97–103.

28.

Sun

Zhao

Hill

(2006) Stability and L₂-gain analysis for switched delay systems: A delay-dependent method. Automatica 42: 1769–1774.

29.

Tang

Wong

(2013) Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Transactions on Neural Networks and Learning Systems 3: 435–447.

30.

Teel

Subbaraman

Sferlazza

(2014) Stability analysis for stochastic hybrid systems: A survey. Automatica 10: 2435–2456.

31.

Xie

Kao

(2015) Delay-dependent robust stability of uncertain neutral-type Itô stochastic systems with Markovian jumping parameters. Applied Mathematics and Computation 251: 576–585.

32.

Lam

(2008) A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Science 12: 1095–1113.

33.

Wang

Gao

Qiu

(2016) A combined fault-tolerant and predictive control for network-based industrial processes. IEEE Transactions on Industrial Electronics 4: 2529–2536.

34.

Wang

Qiu

Guo

(2017) Adaptive neural control of stochastic nonlinear time-delay systems with multiple constraints. IEEE Transations on Systems, Man, and Cybernetics: Systems 8: 1875–1883.

35.

Wang

Zhang

Qiu

et al . (2015) Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements. IEEE Transations on Fuzzy Systems 2: 302–312.

36.

Huang

(2010) Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with unbounded delay. Systems and Control Letters 59: 195–202.

37.

Yan

zbay

(2008) Stability analysis of switched time delay systems. SIAM Journal on Control and Optimization 47: 936–949.

38.

Zhang

Wang

et al . (2017) Sampled-data synchronization analysis of Markovian neural networks with generallly incomplete transition rates. IEEE Transactions on Neural Networks and Learnning Systems 28: 740–752.

39.

Zhang

Boukas

Lam

(2008) Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Transactions on Automatic Control 53: 2458–2464.

40.

Zhou

Ding

Zhou

et al . (2016a) Almost sure adaptive asymptotically synchronization for neutral-type multi-slave neural networks with Markovian jumping parameters and stochastic perturbation. Neurocomputing 214: 44–52.

41.

Zhou

Zhu

Shi

et al . (2014) Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters. IEEE Transactions on Cybernetics 44: 2848–2860.