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Stochastic H2/H∞ control of nonlinear systems with time-delay and state-dependent noise

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  • Gao, Ming
  • Sheng, Li
  • Zhang, Weihai

Abstract

This paper investigates the problem of H2/H∞ control for nonlinear stochastic systems with time-delay and state-dependent noise. Firstly, a sufficient condition for the existence of the nonlinear stochastic H2/H∞ control with time-delay is presented in terms of coupled Hamilton–Jacobi equations (HJEs). Secondly, by using the fuzzy approach, the stochastic H2/H∞ controller can be designed via solving a set of linear matrix inequalities instead of coupled HJEs. Finally, two numerical examples are employed to show the effectiveness of the results obtained.

Suggested Citation

  • Gao, Ming & Sheng, Li & Zhang, Weihai, 2015. "Stochastic H2/H∞ control of nonlinear systems with time-delay and state-dependent noise," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 429-440.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:429-440
    DOI: 10.1016/j.amc.2015.05.090
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    References listed on IDEAS

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    1. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-dependent robust control for uncertain stochastic T–S fuzzy systems with time-varying state and input delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 877-887.
    2. Li Sheng & Ming Gao & Weihai Zhang, 2014. "Dissipative control for Markov jump non-linear stochastic systems based on T–S fuzzy model," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(5), pages 1213-1224, May.
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    Cited by:

    1. Jia, Jinping & Dai, Hao & Zhang, Fandi & Huang, Jianwen, 2022. "Global stabilization of low-order stochastic nonlinear systems with multiple time-varying delays by a continuous feedback control," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. Ziye Zhang & Xiaoping Liu & Chong Lin & Bing Chen, 2018. "Finite-Time Synchronization for Complex-Valued Recurrent Neural Networks with Time Delays," Complexity, Hindawi, vol. 2018, pages 1-14, December.
    3. Xin Guo & Hejun Yao & Fangzheng Gao, 2022. "Global Prescribed-Time Stabilization of High-Order Nonlinear Systems with Asymmetric Actuator Dead-Zone," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
    4. Long, Shaohua & Wu, Yunlong & Zhong, Shouming & Zhang, Dian, 2018. "Stability analysis for a class of neutral type singular systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 113-131.
    5. Shi, Shuang & Fei, Zhongyang & Shi, Zhenpeng & Ren, Shunqing, 2018. "Stability and stabilization for discrete-time switched systems with asynchronism," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 520-536.
    6. Xie, Wenqian & Zhu, Hong & Zhong, Shouming & Zhang, Dian & Shi, Kaibo & Cheng, Jun, 2018. "Extended dissipative estimator design for uncertain switched delayed neural networks via a novel triple integral inequality," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 82-102.
    7. Zhang, He & Xu, Shengyuan & Zhang, Zhengqiang & Chu, Yuming, 2022. "Practical stability of a nonlinear system with delayed control input," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    8. Li, Hongjie & Zhu, Yinglian & jing, Liu & ying, Wang, 2018. "Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 1-15.
    9. Shen, Mouquan & Ye, Dan, 2017. "A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 53-64.

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