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Research Papers

Stabilization of Continuous-Time Fractional Positive Systems With Delays and Asymmetric Control Bounds

[+] Author and Article Information
Abdellah Benzaouia

Physics Department Faculty of Sciences Semlalia,
LAEPT,
Cadi Ayyad University,
P.O. Box 2390,
Marrakesh 40090, Morocco
e-mail: benzaouia@uca.ac.ma

Fouad Mesquine

Physics Department Faculty of Sciences Semlalia,
LAEPT,
Cadi Ayyad University,
P.O. Box 2390,
Marrakesh 40090, Morocco
e-mail: mesquine@uca.ac.ma

Mohamed Benhayoun

Physics Department Faculty of Sciences Semlalia,
LAEPT,
Cadi Ayyad University,
P.O. Box 2390,
Marrakesh 40090, Morocco
e-mail: mbenhayoun@uca.ma

Abdoulaziz Ben Braim

Physics Department Faculty of Sciences Semlalia,
LAEPT,
Cadi Ayyad University,
P.O. Box 2390,
Marrakesh 40090, Morocco
e-mail: azizbenbraim@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 26, 2017; final manuscript received December 28, 2018; published online January 29, 2019. Assoc. Editor: Yunjun Xu.

J. Dyn. Sys., Meas., Control 141(5), 051008 (Jan 29, 2019) (8 pages) Paper No: DS-17-1632; doi: 10.1115/1.4042467 History: Received December 26, 2017; Revised December 28, 2018

Continuous-time fractional linear systems with delays, asymmetrical bounds on control and non-negative states are considered. Hence, the stabilization problem is studied and solved. A direct Lyapunov–Krasovskii function is used leading to conditions in terms of a linear program (LP). Simulation difficulties and numerical problems raised by the use of the Mittag-Leffler expression are overcome. In fact, the obtained solution uses the fractional integration of the system dynamic. Illustrative examples are presented to show the effectiveness of the results. First, a numerical one is given to demonstrate the applicability of the obtained conditions. Second, an application on a real world example is provided to highlight the usefulness of the approach.

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Figures

Grahic Jump Location
Fig. 4

Voltage capacitor evolution in time

Grahic Jump Location
Fig. 1

Closed-loop motions from different initial conditions

Grahic Jump Location
Fig. 2

Evolution of the controls u(t)

Grahic Jump Location
Fig. 5

Control evolution in time

Tables

Errata

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