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International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 759–768 | Cite as

\({\mathscr{H}}_-\) Index for Nonlinear Stochastic Systems with State- and Input-Dependent Noises

  • Yan Li
  • Xikui LiuEmail author
Article

Abstract

This brief focuses on the \(\mathscr {H}_-\) index problem for nonlinear systems involving state- and input-dependent noises in finite and infinite horizon. A sufficient condition of the \(\mathscr {H}_-\) index in finite/infinite case is developed for such systems based on Hamilton–Jacobi equations/inequalities (HJEs/HJIs). Generally, one can hardly solve these HJEs/HJIs. By fuzzy approach, the characterization of \(\mathscr {H}_{-}\) index is derived via solving a linear matrix inequality (LMI). Finally, an example verifies the effect of the obtained results.

Keywords

\(\mathscr {H}_-\) index Nonlinear stochastic systems Fuzzy approach 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61402265); the SDUST Research Fund (2015TDJH105); the Fund for Postdoctoral Application Research Project of Qingdao (01020120607).

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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.College of Electrical Engineering and AutomationShandong University of Science and TechnologyQingdaoChina
  2. 2.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  3. 3.Shandong Province Key Laboratory of Wisdom Mine Information TechnologyShandong University of Science and TechnologyQingdaoChina

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