On Stability of Difference Schemes for a Class of Nonlinear Switched Systems

  • Alexander Aleksandrov
  • Alexey Platonov
  • Yangzhou Chen
Chapter
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9570)

Abstract

The problem of preservation of stability under discretization is studied. A class of nonlinear switched difference systems is considered. Systems of the class appear as computational schemes for continuous-time switched systems with homogeneous right-hand sides. By using the Lyapunov direct method, some sufficient conditions of the asymptotic stability of solutions for difference systems are obtained. These conditions depend on the information available about the switching law. Three cases are considered. In the first case, we can guarantee the asymptotic stability for any switching law, while in the second and in the third ones, classes of switched signals are determined for which the preservation of the asymptotic stability takes place.

Keywords

Switched difference systems Computational schemes Stability Lyapunov functions Dwell-time 
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Notes

Acknowledgments

This work is supported by the St. Petersburg State University (project no. 9.38.674.2013), the Russian Foundation for Basic Research (grant no. 15-58-53017), NSF of China (project no. 61273006), and High Technology Research and Development Program of China (863 Program) (project no. 2011AA110301).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Alexander Aleksandrov
    • 1
  • Alexey Platonov
    • 1
  • Yangzhou Chen
    • 2
  1. 1.Saint Petersburg State UniversitySaint PetersburgRussia
  2. 2.Beijing University of TechnologyBeijingChina

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