  Numerical methods that preserve geometric invariants of the system, such as
energy, momentum or the symplectic form, are called geometric integrators.
Variational integrators are an important class of geometric integrators. The
general idea for those variational integrators is to discretize Hamilton's
principle rather than the equations of motion in a way that preserves some of
the invariants of the original system. In this paper we construct variational
integrators with fixed time step for time-dependent Lagrangian systems
modelling an important class of autonomous dissipative systems. These
integrators are derived via a family of discrete Lagrangian functions each one
for a fixed time-step. This allows to recover at each step on the set of
discrete sequences the preservation properties of variational integrators for
autonomous Lagrangian systems, such as symplecticity or backward error analysis
for these systems. We also present a discrete Noether theorem for this class of
systems. Applications of the results are shown for the problem of formation
stabilization of multi-agent systems.
