Finite-time integral control of nonlinear planar systems subject to mismatched disturbances.

This paper investigates the finite-time bounded control of nonlinear planar systems subject to mismatched disturbances, where the perturbed uncertainties are relaxed to nonlinear functions with low-order terms. By revamping the technique of adding a power integrator and introducing new coordinates, a systematic Lyapunov method is proposed. This is achieved by three major mechanisms: (i) for the purpose of finite-time convergence, a lower-order integral dynamic is first constructed; (ii) a new structural controller is constructed to handle the mismatched disturbances; and (iii) a new structural Lyapunov function is established to provide an effective estimating tool for analyzing the finite-time boundness of the considered systems. A simulation example is given to verify the effectiveness of the proposed controller.