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Research Papers

New Stabilization Schemes for Linear Hybrid Systems With Time-Varying Delays

[+] Author and Article Information
Magdi S. Mahmoud1

Department of Systems Engineering, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran 31261, Saudi Arabiamsmahmoud@kfupm.edu.sa

Sami A. Elferik

Department of Systems Engineering, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran 31261, Saudi Arabiaselferik@kfupm.edu.sa

Throughout this paper, we use the terms hybrid and switched interchangeably to mean one another.

Systems where the dynamical matrices evolve in a polytope defined by its vertices.

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(5), 051007 (Aug 19, 2010) (11 pages) doi:10.1115/1.4002102 History: Received May 21, 2008; Revised April 07, 2010; Published August 19, 2010; Online August 19, 2010

In this paper, we provide new stabilization schemes for a class of linear hybrid time-delay systems under arbitrary switching. These schemes are delay-independent and delay-dependent H stabilization based on proportional-plus-derivative (PPD) feedback strategy. By adopting a selective Lyapunov–Krasovskii functional, new criteria are constructed in a systematic way in terms of feasibility testing of linear matrix inequalities (LMIs). When the time delay is a continuous bounded function, we derive the solution for nominal and polytopic models and identify several existing results as special cases. In case the time delay is a differentiable time-varying function satisfying some bounding relations, we establish a new parametrized LMI characterization for PPD feedback stabilization. The theoretical developments are illustrated on examples of combustion in rocket motor chambers, river pollution control, and resilience analysis, and the ensuing results are compared with the conventional feedback stabilization.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

First state trajectories under PPD and state feedback control

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Figure 2

Second state trajectories under PPD and state feedback control

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Figure 3

Third state trajectories under PPD and state feedback control

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Figure 4

Fourth state trajectories under PPD and state feedback control

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Figure 5

State trajectories: example 2

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Figure 6

Control trajectories: example 2

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