Finite Settling Time Control of Nonlinear Systems in Presence of Matched Perturbations using Barrier Lyapunov Function

In this paper, a novel control method is proposed using barrier Lyapunov function and conventional sliding mode control such that the finite time tracking is achieved. The proposed controller is robust to matched perturbations and a settling time calculation is provided such that the tracking error is within an acceptable value. Furthermore, if output of system is initially in a realistic bound, it is guaranteed to stay in that bound for all future time. The stability analysis of designed controller is presented based on Lyapunov theorem. The simulations are conducted for two numerical examples. In first example, the stabilization of a double integrator without disturbance is considered and phase portrait of states is shown graphically to analyze the controller. In second example, the tracking of single inverted pendulum is simulated in presence of disturbances. The results show the efficacy of the proposed controller.