This paper presents a new family of explicit time integration algorithms with controllable numerical dissipation for structural dynamic problems by utilizing the discrete control theory. Firstly, the equilibrium equation of the implicit Yu- algorithm is adopted, and the recursive formulas of velocity and displacement for the explicit CR algorithm are used in the algorithms. Then, the transfer function and characteristic equation of the algorithms with integration coefficients are obtained by the transformation. Furthermore, their integration coefficients are derived according to the poles condition. It was indicated that the proposed algorithms possess the advantages of second-order accuracy, self-starting, and unconditional stability for linear systems and nonlinear systems with softening stiffness. The numerical dissipation of the algorithms is controlled by the spectral radius at infinity . It was also shown that the proposed algorithms have the same poles as the Yu- algorithm, and thus the same numerical properties. Compared with the implicit Yu- algorithm, the proposed algorithms are explicit in terms of both the displacement and velocity formulas. Finally, the effectiveness of the proposed algorithms in reducing the undesired participation of higher modes for solving the dynamic responses of linear and nonlinear systems has been demonstrated.