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

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • Mohamad S. Alwan

    (University of Waterloo, Department of Applied Mathematics)

  • Xinzhi Liu

    (University of Waterloo, Department of Applied Mathematics)

Abstract

This paper addresses stochastic control system of differential equations with piecewise constant arguments (SEPCA SEPCA ). The piecewise constant arguments are of delay type. The system is viewed as a hybrid Hybrid system (or particularly switched) system Switched systems . 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 ISS ), and H ∞ H ∞ performance for a class of an uncertain control SEPCA. To analyze these result, a common Lyapunov function Lyapunov function together with the techniques of differential inequalities and Razumikhin Razumikhin condition is used. A numerical example with simulations is presented to clarify the validity of the proposed theoretical approaches.

Suggested Citation

  • Mohamad S. Alwan & Xinzhi Liu, 2016. "Input-to-State Stability and H ∞ Performance for Stochastic Control Systems with Piece wise Constant Arguments," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 367-377, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_34
    DOI: 10.1007/978-3-319-30379-6_34
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