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Robust Stability, Stabilization, and Control of a Class of Nonlinear Discrete Time Stochastic Systems

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  • Tianliang Zhang
  • Yu-Hong Wang
  • Xiushan Jiang
  • Weihai Zhang

Abstract

This paper studies robust stability, stabilization, and control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robust performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.

Suggested Citation

  • Tianliang Zhang & Yu-Hong Wang & Xiushan Jiang & Weihai Zhang, 2016. "Robust Stability, Stabilization, and Control of a Class of Nonlinear Discrete Time Stochastic Systems," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-11, April.
    • Handle: RePEc:hin:jnlmpe:5185784
    DOI: 10.1155/2016/5185784
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