Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

  • Quanxin Zhu
  • Fubao Xi
  • Xiaodi Li


In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.


Robust exponential stability Nonlinear system Lyapunov functional Markovian jump parameter Mixed time delay 



This work was jointly supported by the National Natural Science Foundation of China (10801056, 11171024), the Natural Science Foundation of Ningbo (2010A610094) and K.C. Wong Magna Fund in Ningbo University. The authors would like to thank the associate editor and anonymous referees for their helpful comments and valuable suggestions regarding this paper.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsNingbo UniversityNingboChina
  2. 2.Department of MathematicsBeijing Institute of TechnologyBeijingChina
  3. 3.School of Mathematical SciencesShandong Normal UniversityJinanChina

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