Boundary Mittag-Leffler stabilization and disturbance rejection for time fractional ODE diffusion-wave equation cascaded systems

• Published in: Communications in nonlinear science & numerical simulation Vol. 142; p. 108568
• Main Authors: Sun, Jiake, Wang, Junmin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2025
• Subjects: Backstepping method; Galerkin’s method; Mittag-Leffler stability; Sliding mode control; Mittag-Leffler stability; Galerkin’s method; Backstepping method; Sliding mode control
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.108568

This paper investigates the boundary stabilization of time fractional-order ODE cascaded with time fractional-order diffusion-wave equation systems subject to external disturbance. We stabilize the systems by using sliding mode control method and backstepping method. We prove the existence of the generalized solution of the closed-loop systems by Galerkin’s method and successive approximation method. The Mittag-Leffler stability of the systems is proven by Lyapunov method. The numerical simulations are presented to illustrate the validity of the theoretical results. •We investigate the boundary stabilization of time fractional cascaded system.•We designed a state feedback controller to stabilize the cascaded system.•We show the existence of the weak solution for the closed-loop system.•The closed-loop system is shown to be Mittag-Leffler stable.