Globally Fixed-Time High-Order Sliding Mode Control for New Sliding Mode Systems Subject to Mismatched Terms and Its Application

High-order sliding mode (HOSM) control is used for output regulation of uncertain systems with known relative degree. Yet, the traditional HOSM algorithm can only achieve finite-time output regulation for standard integrator sliding mode systems, whose settling time depends on system initial conditions. In this article, first, we extend the standard sliding mode system to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the uncertainties in input channel and/or relax the well-defined relative degree assumption. Second, the conventional constant upper bounds assumption is relaxed to time-varying functions, which enables us to obtain a globally convergent controller. Finally, for the new sliding mode system under the new global assumption, we propose a novel fixed-time HOSM controller whose settling time can be predefined and is free of system initial conditions. In addition, strict Lyapunov analysis is provided to show that the new sliding mode system under the proposed controller and the new global assumption is globally fixed-time stable. An application to buck converter is given to show the effectiveness of the proposed controller.