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In this paper Adams-Bashforth approximations were employed for sampled-data modeling of a large class of vehicle dynamics in many degrees of freedom. The problem of path tracking and regulation with geometric and kinematic specifications on the reference paths was focused afterwards. An approach to model-based controller design was presented based on a Lyapunov method over an incremental functional of the path error energies. Asymptotic convergence for small sampling periods into a residual set with a measure depending only on the one-step-ahead sampled-data model errors was proved. Guidelines to select design matrices for independently tuning of the kinematic and geometric path tracking are provided. A case study for a 6 degrees-of-freedom vehicle illustrates the features of the proposed digital control system.