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.
Stabilization of Continuous-Time Fractional Positive Systems With Delays and Asymmetric Control Bounds
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.
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Benzaouia, A., Mesquine, F., Benhayoun, M., and Ben Braim, A. (January 29, 2019). "Stabilization of Continuous-Time Fractional Positive Systems With Delays and Asymmetric Control Bounds." ASME. J. Dyn. Sys., Meas., Control. May 2019; 141(5): 051008. https://doi.org/10.1115/1.4042467
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