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Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time‐Varying Delays via Output Feedback Control

Author

Listed:
  • Mingzhu Song
  • Wenwen Cheng
  • Quanxin Zhu
  • Hongwei Zhou
  • Hui Wang

Abstract

We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time‐varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time‐varying delays to guarantee that the closed‐loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time‐varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

Suggested Citation

  • Mingzhu Song & Wenwen Cheng & Quanxin Zhu & Hongwei Zhou & Hui Wang, 2016. "Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time‐Varying Delays via Output Feedback Control," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:7548156
    DOI: 10.1155/2016/7548156
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    References listed on IDEAS

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    1. Liang Liu & Zhandong Yu & Qi Zhou & Hamid Reza Karimi, 2013. "State-Feedback Stabilization for a Class of Stochastic Feedforward Nonlinear Time-Delay Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    2. Liang Liu & Ming Gao, 2013. "State Feedback Control for Stochastic Feedforward Nonlinear Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, December.
    3. Liang Liu & Zhandong Yu & Qi Zhou & Hamid Reza Karimi, 2013. "State‐Feedback Stabilization for a Class of Stochastic Feedforward Nonlinear Time‐Delay Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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