A Novel Fixed‐Time Second‐Order Sliding Mode Controller Design Using a Switching Time‐Varying Function

ABSTRACT This article addresses the problem of the globally fixed‐time second‐order sliding mode (SOSM) control for a category of uncertain nonlinear systems, in which the upper bound of the settling time can be arbitrarily prescribed. First, a novel switching time‐varying function (STF) is introduced to effectively circumvent the infinite‐gain issue commonly encountered in the existing prescribed adjustment functions, while remaining continuously differentiable and uniformly bounded over the entire time horizon. By employing the STF‐based coordinate transformation, the SOSM dynamics with a mismatched term are transformed into an equivalent nonlinear system for controller design. Subsequently, by combining the properties of the STF and the improved adding a power integrator technique, a fixed‐time SOSM controller is systematically constructed. Rigorous Lyapunov analysis demonstrates that both the sliding variable and its first‐order derivative are stabilized to the origin within any prescribed settling time, and remain at the equilibrium point thereafter. The distinctive feature of the proposed control framework is that the settling‐time upper bound is completely independent of any system initial conditions and design control parameters, and can be arbitrarily assigned in accordance with the actual requirements of the user. Finally, a representative simulation example is conducted to validate the efficacy of the designed fixed‐time SOSM control strategy.