Robust adaptive fixed-time stabilization of disturbed planar high-order nonlinear systems

In this letter, an adaptive fixed-time integral sliding mode (ISM) controller is exploited for the stabilization of disturbed planar high-order nonlinear systems. The exploited controller is designed by constructing a novel fixed-time ISM surface to tackle the high-order power. Moreover, the parametric adaptive technique is embedded to estimate the square of the upper bound of the disturbance. In this way, the exploited controller has no obvious chattering problem and can maintain the high control accuracy simultaneously. The resultant closed-loop system is proved to be practically fixed-time stable through the bilimit homogeneous theory and fixed-time Lyapunov stability theory. Lastly, two simulated examples are carried out to demonstrate the derived results.