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Integral sliding mode control design for nonlinear stochastic systems under imperfect quantization

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Abstract

This paper presents a sliding mode control (SMC) scheme via output-feedback approach for Itô stochastic systems under a quantization mechanism. The quantization process is formulated with the imperfection that random packet loss occurs at the logarithmic quantizer. A Luenberger observer is designed, based on the packet loss rate and the imperfect quantized measurement. A novel SMC law is synthesized by utilization of an integral sliding surface. The stochastic stability of the resulting closed-loop system is analyzed in terms of Lyapunov stability, and a set of solvable matrix inequalities are established for practical application requirements. Finally, a simulation example is employed for the illustration of the effectiveness of the presented control scheme.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61525303, 61503099), Top-Notch Young Talents Program of China (Ligang Wu), China Postdoctoral Science Foundation Funded Projects (Grant Nos. 2015M570293, 2016T90291), and Self-Planned Task of State Key Laboratory of Robotics and System (HIT) (Grant No. 201713A).

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Correspondence to Ligang Wu.

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Gao, Y., Luo, W., Liu, J. et al. Integral sliding mode control design for nonlinear stochastic systems under imperfect quantization. Sci. China Inf. Sci. 60, 120206 (2017). https://doi.org/10.1007/s11432-017-9148-2

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Keywords

  • stochastic systems
  • quantized control
  • sliding mode control
  • observer design
  • packet loss