Prescribed-time second-order sliding mode controller design subject to mismatched term

This paper investigates the second-order sliding mode (SOSM) control for uncertain nonlinear systems subject to unknown mismatched terms. A new prescribed-time SOSM controller is developed by applying a time-varying coordinate transformation. The proposed controller can allow to prescribe the convergence time a priori and irrespective of initial conditions even in the presence of mismatched terms. Moreover, all the upper bounds of matched and mismatched uncertainties are not required to be exactly known. Finally, a simulation example with different initial conditions is given to show the effectiveness of the proposed controller.