Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control

• Published in: Applied mathematics and computation Vol. 449; p. 127959
• Main Authors: Li, Xing-Yu, Wu, Kai-Ning, Liu, Xiao-Zhen
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-07-2023
• Subjects: Intermittent boundary controller; Mittag–Leffler stabilization; Robust Mittag–Leffler stabilization; Short memory fractional reaction-diffusion systems; Short memory fractional reaction-diffusion systems; Mittag–Leffler stabilization; Intermittent boundary controller; Robust Mittag–Leffler stabilization
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2023.127959

•An appropriate intermittent boundary controller is designed which is different from the existing controller designed in references.•The designed controller can exponentially stabilize FRDSs at a desired convergent rate, even though FRDSs are naturally exponentially stable or unstable.•The exponential stabilization for uncertain FRDSs with parameter uncertainties is considered under the intermittent boundary controller.•The theoretical results expose how the control gains and diffusion coefficient matrix affect the stability.
Under the designed intermittent boundary controller, the Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems (SMFRDSs) is investigated. By employing the Lyapunov functional method and kinds of inequalities, we derive a sufficient criterion that ensures the Mittag–Leffler stability for SMFRDSs. Robust Mittag–Leffler stability is also considered when there are uncertainties in SMFRDSs. Besides, we analyze how the control gains and diffusion coefficient matrix affect the stability. Finally, we carry out the numerical simulation based on the above results.