Abstract
This paper considers observer-based output feedback stabilization and stability robustness against small diffusivity perturbations of coupled time fractional partial differential equations (PDEs) with space-dependent (non-constant) parameters. Herein, the plant is equipped with the only available measurement at x=0 and actuation at x=1 . By backstepping transformation, the well-posedness of the kernel matrix PDE and the observer gains are obtained. Then an output feedback controller is introduced and the Mittag-Leffler stability of the closed-loop system is proved by the fractional Lyapunov method. Robustness analysis of diffusion coefficients uncertainty (with a small perturbation in the diffusion coefficient) is also provided. The output feedback stabilization of the closed-loop system is tested by a numerical example.
Highlights
(2) Robustness to a small perturbation in diffusion coefficients: The most striking feature in stability robustness analysis is that we prove the robustly Mittag-Leffler stability of the closed-loop system with the proposed output feedback controller, which is nontrivial for integer-order partial differential equations (PDEs) systems [20], [21]
ROBUSTNESS TO UNCERTAINTY DIFFUSIVITY We investigate the robustness of the output feedback controller (37) to a small perturbation in diffusion coefficients for the coupled time fractional PDE system
CONCLUDING REMARKS We investigated observer-based output feedback stabilization and robustness analysis to small diffusivity perturbations of coupled time fractional PDEs with spatially varying coefficients by backstepping
Summary
There exists some limitation of technology for sensors capturing dynamics feature, which leads us to obtain full state information unavailable In this case, an observer-based output feedback control design method is used to overcome this deficiency. Transformation to deal with output feedback stabilization and stability robustness against small diffusivity perturbations of coupled non-constant parameter time fractional PDEs. Recently, the work [11] designed the Mittag-Leffler convergent observer for its output feedback stabilization of coupled fractional semilinear PDEs. Therein, in order to obtain an explicit solution of the kernel PDE, they transformed the spatially varying parameters into constant ones by an appropriate transformation and added the assumption of the diagonal kernel matrix function. We claim that our results in this paper are still novel and even open a door for stability robustness of coupled time fractional systems
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
