Fixed‐time stabilization for lower‐triangular nonlinear systems with low‐order and high‐order nonlinearities

Abstract This paper investigates the problem of fixed‐time stabilization for a class of lower‐triangular nonlinear systems with high‐order and low‐order nonlinearities. A novel fixed‐time stabilization method is proposed based on an improved gain scaling technique, which features three dynamic parameters that adjust the controller gain in real time. Different from classical iterative design methods based on backstepping, the proposed method avoids the cumbersome iterative design procedures. First, combining the original system states and the dynamic parameters, the auxiliary variables are defined through state transformation, which converts the controller design problem for the considered system into the dynamic parameter design problem for an equivalent system. Subsequently, employing the Lyapunov stability theory, the state‐feedback controller based on dynamic parameters are meticulously designed to achieve the fixed‐time stabilization of the closed‐loop system. It is worth noting that the resulting controller has a simple quasi‐linear form and can be explicitly expressed by the closed‐loop system states. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control method.