A Novel Terminal Sliding Mode Control with Robust Prescribed-Time Stability

The present paper investigates a new tool for analyzing stability/convergence properties and robustness against matched perturbations of a class of nonlinear systems. We start with a scalar system, where it is shown that the state can be regulated or stabilized to a prescribed time using time-varying functions. The proof is based on Lyapunov theory. We developed a robust terminal-integral sliding mode controller that guarantees convergence of the system states to a desired equilibrium within a user-defined time, irrespective of initial conditions and under bounded disturbances. The method was extended to a class of second-order nonlinear systems, achieving both fixed-time (prescribed-time) convergence and robustness. Theoretical properties were established via Lyapunov-based analysis, and numerical simulations confirmed the effectiveness of the proposed methods in terms of robustness and convergence.