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 method-ology 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 in-equalities (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 re-quirement 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, simula-tion studies are presented to confirm the efficacy and robustness of proposed approach.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this study, a novel barrier function-based adaptive non-singular terminal sliding mode control methodology is proposed to ensure the robust stability of disturbed nonlinear systems. It is proven that the barrier function-based control method can drive the state trajectories to converge to a region near the origin within a finite time. A sufficient criterion is derived using Lyapunov stability theorem and linear matrix inequalities (LMIs) to satisfy the asymptotic stability of state trajectories. Moreover, the design eliminates the need for any knowledge about the upper bounds of external disturbances, which is a common requirement in sliding mode control implementation. The stability analysis confirms that the system states, under the designed control scheme, can asymptotically converge to a predefined region. Simulation studies are presented to validate the effectiveness and robustness of the proposed approach.