fixed-time stability

In this article, time-varying chaotic systems with uncertainties, including external disturbances, are considered, and sliding mode control (SMC) is used to control such systems. To control these systems, an autonomous differential equation is first introduced. Then, based on this differential equation, a sliding surface is defined to control this chaotic system. This kind of controller is remarkable in that it removes the effects of disturbances, whether bounded or unbounded. Therefore, the system is known to be fixed-time stable. where the trajectories of this chaotic system are not placed on the sliding surface, we have created creative controllers to place the trajectories on the sliding surface in finite time. Theoretical investigations show that such chaotic systems can be made fixed-time stable by applying the controls proposed in this study. Based on the findings of this study, the controllers are designed to eliminate all disturbances, whether bounded or unbounded. the results be said to apply chaotic, time-dependent, and time-independent systems. To further consolidate the results obtained in this article, two examples, namely the time-dependent system of the Gyro and the time-independent system of the Liu, are investigated, and the results were compared with previous works by other researchers.

This paper investigates fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems in the presence of matched and mismatched disturbances. Using estimation of the mismatched disturbance estimated by a fixed-time disturbance observer, a novel nonlinear dynamic sliding surface is designed. This estimation is utilized in designing a completely novel nonlinear dynamics sliding surface whereby the fixed-time convergence of the sliding motion is guaranteed in spite of mismatched disturbance. The convergence time of the closed-loop system including disturbance observer and control system is guaranteed to be uniform with respect to initial conditions. Moreover, the proposed controller avoids chattering phenomenon by producing a continuous control signal.