Abstract
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.
Original language | English |
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Article number | 108568 |
Journal | Communications in Nonlinear Science and Numerical Simulation |
Volume | 142 |
DOIs | |
Publication status | Published - Mar 2025 |
Keywords
- Backstepping method
- Galerkin's method
- Mittag-Leffler stability
- Sliding mode control