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Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays

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  • M. 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 LMIs. We characterize decentralized linear matrix inequalities (LMIs)-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with a γ-level ℒ2-gain. The developed results are tested on a representative example.

Suggested Citation

  • M. S. Mahmoud, 2009. "Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 497-518, December.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:3:d:10.1007_s10957-009-9571-y
    DOI: 10.1007/s10957-009-9571-y
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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.
    3. Chen, Zhaohui & Huang, Qi & Liu, Zhang, 2015. "Decentralized finite-time H∞ filtering for interconnected Markovian jump system with interval mode-dependent delays," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 138-154.

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