Title: Mittag-Leffler stability analysis for time-fractional hyperbolic systems with space-dependent reactivity using backstepping-based boundary control

Authors: Yanjiu Zhou; Baotong Cui; Bo Zhuang; Juan Chen

Addresses: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of IoT Engineering, Jiangnan University, Wuxi, 214122, Jiangsu, China ' Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of IoT Engineering, Jiangnan University, Wuxi, 214122, Jiangsu, China ' School of Information Engineering, Binzhou University, Binzhou, 256600, Shandong, China ' Aliyun School of Big Data, Changzhou University, Changzhou, 213164, Jiangsu, China

Abstract: This paper presents the Mittag-Leffler stability analysis for a controlled time-fractional hyperbolic system with space-dependent reactivity via the backstepping method. The main work of this paper is divided into two parts: 1) the backstepping-based boundary controller design to deal with unstable source terms; 2) the Mittag-Leffler stability analysis by the time-fractional Lyapunov method. For the numerical solution, the implicit Euler finite difference method is applied, together with the family of characteristic curves to solve the kernel partial differential equation and the method of discretising the Caputo time-fractional derivative. Finally, two examples are given to illustrate the accuracy of the algorithm for calculating the kernel function by contrast with corresponding analytic solutions. A numerical example is shown to validate the effectiveness of the proposed controller.

Keywords: Mittag-Leffler stability; time-fractional hyperbolic system; backstepping; boundary control.

DOI: 10.1504/IJMIC.2023.132106

International Journal of Modelling, Identification and Control, 2023 Vol.43 No.1, pp.1 - 12

Received: 28 Mar 2022
Received in revised form: 11 Aug 2022
Accepted: 13 Aug 2022
Published online: 11 Jul 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article