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research-article

Stabilization of Continuous-time Fractional Positive Systems with Delays and Asymmetric Control Bounds

[+] Author and Article Information
Abdellah Benzaouia

LAEPT, Physics Dep. Faculty of Sciences Semlalia, Cadi Ayyad University, PoBox. 2390, Marrakesh, Morocco
benzaouia@uca.ac.ma

Fouad Mesquine

LAEPT, Physics Dep. Faculty of Sciences Semlalia, Cadi Ayyad University, PoBox. 2390, Marrakesh, Morocco
mesquine@uca.ac.ma

Mohamed Benhayoun

LAEPT, Physics Dep. Faculty of Sciences Semlalia, Cadi Ayyad University, PoBox. 2390, Marrakesh, Morocco
mbenhayoun@uca.ma

Abdoulaziz Benbraim

LAEPT, Physics Dep. Faculty of Sciences Semlalia, Cadi Ayyad University, PoBox. 2390, Marrakesh, Morocco
azizbenbraim@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4042467 History: Received December 26, 2017; Revised December 28, 2018

Abstract

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. Direct Lyapunov-Krasovskii function is used leading to conditions in terms of a linear program. 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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