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Stability of nonlinear impulsive stochastic systems with Markovian switching under generalized average dwell time condition

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Abstract

This paper examines the p-th moment globally asymptotic stability in probability and p-th moment stochastic input-to-state stability for a type of impulsive stochastic system withMarkovian switching. By applying the generalized average dwell time approach, some novel sufficient conditions are obtained to ensure these stability properties. Furthermore, the coefficient of the Lyapunov function is allowed to be time-varying, which generalizes and improves the existing results. As corollaries, nonlinear restrictions on the drift and diffusion coefficients are used as substitutes for some previous conditions. Two examples are provided to illustrate the effectiveness of the theoretical results.

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Acknowledgements

This work was jointly supported by National Natural Science Foundation of China (Grant Nos. 61773217, 61374080), Natural Science Foundation of Jiangsu Province (Grant No. BK20161552), Qing Lan Project of Jiangsu Province, and Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Correspondence to Quanxin Zhu.

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Fu, X., Zhu, Q. Stability of nonlinear impulsive stochastic systems with Markovian switching under generalized average dwell time condition. Sci. China Inf. Sci. 61, 112211 (2018). https://doi.org/10.1007/s11432-018-9496-6

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Keywords

  • generalized average dwell time condition
  • impulsive stochastic system
  • Markovian switching
  • time-varying coefficient
  • input-to-state stability
  • nonlinear restrictions