Stabilization of a Class of Fractional-Order Nonlinear Systems Subject to Actuator Saturation and Time Delay

Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order (FO) nonlinear systems under these two practical constraints. Two primary methodologies are employed: the vector Lyapunov function method, integrated with the M-matrix approach, and the second one is the Lyapunov-like function method, which incorporates diffusive realization and the Lipchitz condition. An optimization framework is proposed to design stabilizing controllers based on the derived stability conditions. The proposed methods are validated numerically through their application to the FO Lorenz and Liu systems, demonstrating their effectiveness in handling actuator saturation and time delay.