In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering and undesirable vibration effects. The advantages of the proposed control method are rapid convergence to the equilibrium point, the absence of chattering and unwanted oscillations, high resistance to uncertainties, and the possibility of applying this method to most fractional order chaotic systems. We applied the direct method of Lyapunov stability theory and the frequency distributed model to prove the stability of the slip surface and closed loop system. Finally, we simulated this method on two commonly used and practical chaotic systems and presented the results.

在这项研究中，我们研究了具有模型不确定性和外部干扰的分数阶混沌非线性动力系统的稳定性。我们通过一种新方法使用滑模控制器来控制和稳定这些系统。在这项研究中，我们在控制器设计和滑动表面中用符号函数代替了连续函数，以抑制震颤和不良的振动影响。所提出的控制方法的优点是可以快速收敛到平衡点，没有颤动和不必要的振荡，对不确定性具有很高的抵抗力，并且可以将此方法应用于大多数分数阶混沌系统。我们应用Lyapunov稳定性理论的直接方法和频率分布模型来证明滑移面和闭环系统的稳定性。最后，我们在两个常用且实用的混沌系统上对该方法进行了仿真，并给出了结果。