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Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science pp 21–27Cite as

Input-to-State Stability of Large-Scale Stochastic Impulsive Systems with Time Delay and Application to Control Systems

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 117))

Abstract

This chapter deals with large-scale nonlinear delay stochastic systems where the system states are subject to impulsive effects and perturbed by some disturbance input having bounded energy. The interest is to develop a comparison principle and establish input-to-state stability (ISS) in the mean square (m.s.) using vector Lyapunov function and Razumikhin technique. Impulses are being viewed as perturbation to stable systems, and they have a stabilizing role to unstable systems.

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References

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Acknowledgments

The research was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    M. S. Alwan, X. Z. Liu & W.-C. Xie

Authors
  1. M. S. Alwan
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  2. X. Z. Liu
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  3. W.-C. Xie
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Corresponding author

Correspondence to M. S. Alwan .

Editor information

Editors and Affiliations

  1. Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada

    Monica G. Cojocaru

  2. Dept of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Department of Mathematics and MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman N. Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roderick V. N. Melnik

  5. MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Hasan Shodiev

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Alwan, M., Liu, X., Xie, WC. (2015). Input-to-State Stability of Large-Scale Stochastic Impulsive Systems with Time Delay and Application to Control Systems. In: Cojocaru, M., Kotsireas, I., Makarov, R., Melnik, R., Shodiev, H. (eds) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. Springer Proceedings in Mathematics & Statistics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-12307-3_4

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