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Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

Author

Listed:
  • Lianglin Xiong
  • Xiaobing Zhou
  • Jie Qiu
  • Jing Lei

Abstract

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.

Suggested Citation

  • Lianglin Xiong & Xiaobing Zhou & Jie Qiu & Jing Lei, 2012. "Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-22, October.
    • Handle: RePEc:hin:jnlaaa:450168
    DOI: 10.1155/2012/450168
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    Cited by:

    1. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin & Wu, Tao & Zhang, Haiyang, 2021. "Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    3. Karthick, S.A. & Sakthivel, R. & Ma, Y.K. & Leelamani, A., 2020. "Observer based guaranteed cost control for Markovian jump stochastic neutral-type neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    4. Jinlong Shu & Lianglin Xiong & Tao Wu & Zixin Liu, 2019. "Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay," Mathematics, MDPI, vol. 7(1), pages 1-23, January.

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