Stabilizability of Riccati Matrix Fractional Delay Differential Equation

Ibtisam Kamil Hanan; Fatimah Al-Taie; Fadhel S. Fadhel

doi:10.24996/ijs.2023.64.4.32

Authors

Ibtisam Kamil Hanan Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
Fatimah Al-Taie Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
Fadhel S. Fadhel Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.4.32

Keywords:

Backstepping method, Method of steps, Mittag-Leffler stabilization, Caputo fractional derivative, Riccati matrix differential equation

Abstract

In this article, the backstepping control scheme is proposed to stabilize the fractional order Riccati matrix differential equation with retarded arguments in which the fractional derivative is presented using Caputo's definition of fractional derivative. The results are established using Mittag-Leffler stability. The fractional Lyapunov function is defined at each stage and the negativity of an overall fractional Lyapunov function is ensured by the proper selection of the control law. Numerical simulation has been used to demonstrate the effectiveness of the proposed control scheme for stabilizing such type of Riccati matrix differential equations.