Abstract and Applied Analysis

Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

Li Liang

Abstract

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 597298, 8 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412605771

Digital Object Identifier
doi:10.1155/2014/597298

Mathematical Reviews number (MathSciNet)
MR3173282

Citation

Liang, Li. Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 597298, 8 pages. doi:10.1155/2014/597298. https://projecteuclid.org/euclid.aaa/1412605771

References

• O. M. Kwon and J. H. Park, “Exponential stability analysis for uncertain neural networks with interval time-varying delays,” Applied Mathematics and Computation, vol. 212, no. 2, pp. 530–541, 2009.
• J. H. Park and O. M. Kwon, “Further results on state estimation for neural networks of neutral-type with time-varying delay,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 69–75, 2009.
• D. Zhang and L. Yu, “Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays,” Neural Networks, vol. 35, pp. 103–111, 2012.
• D. Zhang, L. Yu, Q. Wang, and C. Ong, “Estimator design fordiscrete-time switched neural networks with asynchronous switching and time-varying delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 5, pp. 827–834, 2012.
• D. Zhang and L. Yu, “Passivity analysis for discrete-time swit-ched neural networks with various activation functions and mixed time delays,” Nonlinear Dynamics, vol. 67, no. 1, pp. 403–411, 2012.
• C.-Y. Lu, W.-J. Shyr, K.-C. Yao, and D.-F. Chen, “Delay-depend-ent approach to robust stability for uncertain discretestochastic recurrent neural networks with interval time-varying delays,” ICIC Express Letters, vol. 3, no. 3, pp. 457–464, 2009.
• Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay,” Neurocomputing, vol. 74, no. 10, pp. 1626–1631, 2011.
• P. Balasubramaniam and G. Nagamani, “Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays,” Expert Systems with Applications, vol. 39, no. 1, pp. 732–742, 2012.
• X. Luan, F. Liu, and P. Shi, “Neural network based stochastic opt-imal control for nonlinear Markov jump systems,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 8, pp. 3715–3724, 2010.
• R. Mei, Q.-X. Wu, and C.-S. Jiang, “Neural network robust adap-tive control for a class of time delay uncertain nonlinear sys-tems,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 3, pp. 931–940, 2010.
• Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Passivity analysis for discr-ete-time stochastic markovian jump neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 22, no. 10, pp. 1566–1575, 2011.
• D. Zhang and L. Yu, “Passivity analysis for stochastic Markovianswitching genetic regulatory networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2985–2992, 2011.
• Z. Wu, P. Shi, H. Su, and J. Chu, “Stochastic synchronization ofMarkovian jump neural networks with time-varying delay using sampled-data,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1796–1806, 2013.
• H. Dong, Z. Wang, and H. Gao, “Fault detection for Markovian jump systems with sensor saturations and randomly varying nonlinearities,” IEEE Transactions on Circuits and Systems I, vol. 59, no. 10, pp. 2354–2362, 2012.
• Z. Wang, Y. Liu, and X. Liu, “Exponential stabilization of a classof stochastic system with Markovian jump parameters and mode-dependent mixed time-delays,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1656–1662, 2010.
• Z. Wu, H. Su, and J. Chu, “State estimation for discrete Marko-vian jumping neural networks with time delay,” Neurocomputing, vol. 73, no. 10–12, pp. 2247–2254, 2010.
• Q. Zhu and J. Cao, “Robust exponential stability of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1314–1325, 2010.
• H. Shen, S. Xu, J. Lu, and J. Zhou, “Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays,” Journal of the Franklin Institute, vol. 349, no. 5, pp. 1665–1680, 2012.
• L. Zhang and E.-K. Boukas, “Stability and stabilization of Mark-ovian jump linear systems with partly unknown transition pro-babilities,” Automatica, vol. 45, no. 2, pp. 463–468, 2009.
• L. Zhang and E.-K. Boukas, “Mode-dependent ${H}_{\infty }$ filtering fordiscrete-time Markovian jump linear systems with partly unknown transition probabilities,” Automatica, vol. 45, no. 6, pp. 1462–1467, 2009.
• H. Dong, Z. Wang, and H. Gao, “Distributed filtering for a class of time-varying systems over sensor networks with quantization errors and successive packet dropouts,” IEEE Transactions on Signal Processing, vol. 60, no. 6, pp. 3164–3173, 2012.
• H. Dong, Z. Wang, and H. Gao, “Distributed H-infinity filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Elecronics, vol. 60, no. 10, pp. 4665–4672, 2013.
• H. Shen, S. Xu, J. Zhou, and J. Lu, “Fuzzy ${H}_{\infty }$ filtering fornonlinear Markovian jump neutral systems,” International Journal of Systems Science, vol. 42, no. 5, pp. 767–780, 2011.
• Z. Zuo, H. Li, Y. Liu, and Y. Wang, “On finite-time stochastic stability and stabilization of Markovian jump systems subject topartial information on transition probabilities,” Circuits, Systems, and Signal Processing, vol. 31, no. 6, pp. 1973–1983, 2012.
• W. Xiang and J. Xiao, “${H}_{\infty }$ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 331–352, 2011.
• L. Zhu, Y. Shen, and C. Li, “Finite-time control of discrete-time systems with time-varying exogenous disturbance,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 361–370, 2009.
• X. Huang, W. Lin, and B. Yang, “Global finite-time stabilization of a class of uncertain nonlinear systems,” Automatica, vol. 41, no. 5, pp. 881–888, 2005.
• C. Qian and J. Li, “Global finite-time stabilization by output feedback for planar systems without observable linearization,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 885–890, 2005.
• J. Cheng, H. Zhu, S. Zhong, Y. Zeng, and L. Hou, “Finite-timeH-infinity filtering for a class of discrete-time Markovian jumpsystems with partly unknown transition probabilities,” International Journal of Adaptive Control and Signal Processing, 2013.
• S. He and F. Liu, “Stochastic finite-time boundedness of Mark-ovian jumping neural network with uncertain transition probabilities,” Applied Mathematical Modelling, vol. 35, no. 6, pp. 2631–2638, 2011.
• H. Song, L. Yu, D. Zhang, and W.-A. Zhang, “Finite-time ${H}_{\infty }$ control for a class of discrete-time switched time-delay systems with quantized feedback,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4802–4814, 2012.
• Y. Yang, J. Li, and G. Chen, “Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects,” Journal of Systems Engineering and Electronics, vol. 21, no. 2, pp. 254–260, 2010.
• S. He and F. Liu, “Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters,” Neurocomputing, vol. 103, pp. 87–92, 2013.
• X. Luan, F. Liu, and P. Shi, “Finite-time filtering for non-linear stochastic systems with partially known transition jump rates,” IET Control Theory & Applications, vol. 4, no. 5, pp. 735–745, 2010.
• F. Amato, M. Ariola, and C. Cosentino, “Finite-time control of discrete-time linear systems: analysis and design conditions,” Automatica, vol. 46, no. 5, pp. 919–924, 2010.
• J. Cheng, H. Zhu, S. Zhong, Y. Zhang, and Y. Li, “Finite-time H-infinity control for a class of discrete-time Markov jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching,” International Journal of Systems Science, 2013.
• J. Cheng, H. Zhu, S. Zhong, F. Zheng, and K. Shi, “Finite-timeboundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching,” Canadian Journal of Physics, vol. 91, pp. 1–9, 2013.
• J. Cheng, H. Zhu, S. Zhong, Y. Zeng, and X. Dong, “Finite-timeH-infinity control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals,” ISA Transactions, vol. 52, pp. 768–774, 2013.
• X. Lin, H. Du, and S. Li, “Finite-time boundedness and ${L}_{2}$-gain analysis for switched delay systems with norm-bounded disturbance,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5982–5993, 2011. \endinput