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Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures

Author

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  • Ali Y. Al-Rayyah

    (King Fahd University of Petroleum and Minerals)

  • Magdi S. Mahmoud

    (King Fahd University of Petroleum and Minerals)

Abstract

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state-measurement and the second utilizes static output-feedback. The decentralized feedback gains in both schemes are determined by convex optimization over linear matrix inequalities. We characterize decentralized linear matrix inequality-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with an γ-level ℒ2-gain. The developed results are tested on a representative example.

Suggested Citation

  • Ali Y. Al-Rayyah & Magdi S. Mahmoud, 2010. "Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 318-336, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9724-z
    DOI: 10.1007/s10957-010-9724-z
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    Cited by:

    1. Y. Y. Wang & P. F. Zhou & Q. B. Wang & D. P. Duan, 2014. "State Estimation and Reliable Control of Singular Markovian Systems with Distributed State Delays and Input Delays," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 313-328, July.
    2. Tri Tran & Q. P. Ha, 2014. "Decentralized Model Predictive Control for Networks of Linear Systems with Coupling Delay," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 933-950, June.

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