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Input-to-State Stability and H ∞ Performance for Stochastic Control Systems with Piece wise Constant Arguments

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Mathematical and Computational Approaches in Advancing Modern Science and Engineering

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Abstract

This paper addresses stochastic control system of differential equations with piecewise constant arguments (SEPCA ). The piecewise constant arguments are of delay type. The system is viewed as a hybrid (or particularly switched) system . This approach motivates the applicability of the classical theory of ordinary differential equations, but not of functional differential equations, and the design of a switching law. The main theme of this work is to establish the problems of input-to-state stabilization (ISS ), and H ∞ performance for a class of an uncertain control SEPCA. To analyze these result, a common Lyapunov function together with the techniques of differential inequalities and Razumikhin condition is used. A numerical example with simulations is presented to clarify the validity of the proposed theoretical approaches.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Mohamad S. Alwan & Xinzhi Liu

Authors
  1. Mohamad S. Alwan
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  2. Xinzhi Liu
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Corresponding author

Correspondence to Mohamad S. Alwan .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Montreal, Montreal, Québec, Canada

    Jacques Bélair

  2. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada

    Ian A. Frigaard

  3. Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada

    Herb Kunze

  4. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman Makarov

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

    Roderick Melnik

  6. Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

    Raymond J. Spiteri

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Alwan, M.S., Liu, X. (2016). Input-to-State Stability and H ∞ Performance for Stochastic Control Systems with Piece wise Constant Arguments. In: Bélair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R. (eds) Mathematical and Computational Approaches in Advancing Modern Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30379-6_34

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