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

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. 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.