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

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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.

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Authors and Affiliations

  1. Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran, 31261, Saudi Arabia

    Ali Y. Al-Rayyah & Magdi S. Mahmoud

Authors
  1. Ali Y. Al-Rayyah
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  2. Magdi S. Mahmoud
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Correspondence to Magdi S. Mahmoud.

Additional information

Communicated by F. Udwadia.

The work of M.S. Mahmoud is supported by KFUPM research project No. FT090015.

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Al-Rayyah, A.Y., Mahmoud, M.S. Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures. J Optim Theory Appl 147, 318–336 (2010). https://doi.org/10.1007/s10957-010-9724-z

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  • DOI: https://doi.org/10.1007/s10957-010-9724-z

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