  The Ostrogradsky instability of higher derivative Lagrangians is derived from
first principles using Control theory and Lyapunov Stability Analysis. This
result is then used to argue that Born-Infeld Lagrangians are viable
modifications of the Einstein-Hilbert action provided the action is varied in
accordance with the Palatini formalism, in contrast to the metric formalism.
Finally, the Born-Infeld version of the FRW equations are derived and the
cosmological dynamics is studied for matter dominated closed and open
universes, and the results are compared with the usual cosmology.
