Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach

In this study, a novel barrier function-based adaptive non-singular terminal sliding mode control methodology is suggested for robust stability of disturbed nonlinear systems. It is proved that the barrier function-based control method can force the state trajectories to converge to a region near origin in the finite time. A sufficient criterion is derived using Lyapunov stability theorem and linear matrix inequalities (LMIs) to satisfy the asymptotic stability of state trajectories. In addition, the design eliminates the necessity to have any knowledge about the upper bounds of external disturbances; a common requirement in sliding mode control implementation. The stability analysis verifies that the system states, under the designed control scheme, can asymptotically converge to a pre-defined region. Lastly, simulation studies are presented to confirm the efficacy and robustness of proposed approach.