The fourth-order model of the reaction wheel pendulum is considered and a fourth-order discontinuous integral algorithm is used for stabilization and tracking of the system, using a continuous control signal. The states reach the origin or a reference signal in finite-time, even in presence of uncertain control coefficient and a kind of matched and unmatched uncertainties/disturbances. A homogeneous Lyapunov function is designed to ensure local finite-time stability of the system, which can be used for designing the controller gains. Simulations and experimental results illustrate the performance and advantages of the presented algorithm. K E Y W O R D S finite-time convergence, higher-order sliding-mode control, nonlinear control, tracking control, wheel pendulum Abbreviations: 3-DIA, third order discontinuous integral algorithm; 4-DIA, fourth order discontinuous integral algorithm; RWP, reaction wheel pendulum.