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Practical ϕ 0-stability of switched stochastic nonlinear systems and corresponding stochastic perturbation theory

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Abstract

The aim of this paper is to study the practical ϕ 0-stability in probability (Pϕ 0SiP) and practical ϕ 0-stability in pth mean (Pϕ 0SpM) of switched stochastic nonlinear systems. Sufficient conditions on such practical properties are obtained by using the comparison principle and the cone-valued Lyapunov function methods. Also, based on an extended comparison principle, a perturbation theory of switched stochastic systems is given.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan Shandong, 250022, China

    Yan Zhao

  2. School of Electrical Engineering, University of Jinan, Jinan Shandong, 250022, China

    Ping Zhao

Authors
  1. Yan Zhao
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  2. Ping Zhao
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Correspondence to Ping Zhao.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 60904024, 61074021), the Shandong Province Natural Science Foundation for Distinguished Young Scholars (No. JQ201119), and the Doctoral Foundation of University of Jinan (No. XBS1012).

Yan ZHAO received her B.S. degree from the University of Jinan, China, in 2002, M.S. degree from the Qufu Normal University, China, in 2005. She is currently a lecturer of University of Jinan. Her research interest is in the stability theory of nonlinear systems.

Ping ZHAO received his B.S. degree from the University of Jinan, China, in 2002, M.S. degree from the Qufu Normal University, China, in 2005, and Ph.D. from Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He is currently a lecturer of University of Jinan. His research interests are in the stability theory and control of stochastic and nonlinear systems.

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Zhao, Y., Zhao, P. Practical ϕ 0-stability of switched stochastic nonlinear systems and corresponding stochastic perturbation theory. J. Control Theory Appl. 11, 92–95 (2013). https://doi.org/10.1007/s11768-013-1115-1

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  • DOI: https://doi.org/10.1007/s11768-013-1115-1

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