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Finite-Time Controllers for a Class of Planar Nonlinear Systems With Mismatched Disturbances

This letter considers the problem of globally finite-time stabilizing a planar nonlinear system with a mismatched unknown disturbance. First, a nonlinear integral dynamic is constructed to compensate the disturbance. For finite-time convergence, we use the system states and integral state to construct a new controller which not only is homogeneous with a negative degree but also contains a linear combination of states to handle the unmatched disturbance. The finite-time integral controller originally obtained for a linear planar system is appropriately scaled to regulate a nonlinear planar system within the framework of homogeneous domination. In addition, for a faster convergence speed for any initial condition, a dual-mode integral controller is introduced with better performances demonstrated by simulation studies.