Abstract: The trajectory-tracking control problem for mobile robot is considered,and the trajectory tracking problem is transformed into the state stabilization problem of error-system through coordinate transformation.A compound finite-time tracking control linearization algorithm based on feedback linearization and variable structure is proposed,the reachingcontrol law is firstly used to drive the steering angle trajectory with initial error to quickly converge to the neighborhood of given switching surface,and then the steering angle error is stabilized quickly by a chattering-free control law based on continuous-time state-feedback,while the nonlinear system is converted into a reduced system.The state-feedback control law for the reduced-rank system is designed to stabilize the position error in finite time.For the error-system with system noise and measurement noise,extended Kalman filter(EKF) is used to estimate the states of the error-system,and the estimated states are used to construct the feedback control law.Numerical simulations show the effectiveness of the control scheme.