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Switched Singularly Perturbed Systems with Reliable Controllers

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)

  • Taghreed G. Sugati

    (University of Waterloo, Department of Applied Mathematics)

Abstract

This paper addresses the problem of exponential stability for a class of switched Switched control singularly perturbed Singularly perturbed systems (SCSPS) not only when all the control actuators are operational, but also when some of them experience failures. Multiple Lyapunov functions Multiple Lyapunov functions and average dwell-time switching signal approach are used to establish the stability criteria for the proposed systems. In this paper, we assume that a full access to all the system modes is available, though the mode-dependent, slow-state feedback controllers experience faulty actuators of an outage type. In the stability analysis, the system under study is viewed as an interconnected system that has been decomposed into isolated, lower order, slow and fast subsystems, and the interconnection between them. It has been observed that if the degree of stability of each isolated mode is greater than the interconnection between them, the interconnected mode is exponentially stable, and, then, the full order SCSPS is also exponentially stable for all admissible switching signals with average dwell-time. A numerical example with simulations is introduced to illustrate the validity of the proposed theoretical results.

Suggested Citation

  • Mohamad S. Alwan & Xinzhi Liu & Taghreed G. Sugati, 2016. "Switched Singularly Perturbed Systems with Reliable Controllers," 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 379-388, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_35
    DOI: 10.1007/978-3-319-30379-6_35
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