Hassan and Amin (1987) and Amin and Hassan (1987) have presented a simple algebraic solution for the ‘time-optimal output deadbeat’ (TOOD) regulator problem. This solution, which consists of a state feedback control law, has been obtained for right-invertible systems. These results are generalized here to accom- modate all classes of output-controllable left-invertible systemsS(A, B, C, E).The design of TOOD regulators with internal stability for all classes of right- or output- controllable left-invertible systemsS(A, B, C, E) is also considered. It is shown that the right Wiener-Hopf factorization at infinityof H(z)—the transfer function matrix ofS—is the key tool for solving all TOOD regulator problems. Moreover, the internal stability problem, which will arise if any invariant zero ofSis unstable, is solved by designing a TOOD regulator with internal stability. Finally, numerical examples are worked out to illustrate the generality of the proposed method.