  We confirm the stability of Podolsky's generalized electrodynamics by
constructing a series of two-parametric bounded conserved quantities which
includes the canonical energy-momentum tensors. In addition, we evaluate the
transition-amplitude of this higher derivative system in BV antifield formalism
and obtain the desirable generalized radiation gauge condition by choosing
appropriate gauge-fixing fermion. Within the framework of Lagrangian BRST
cohomology, we present the constructions of consistent interactions in
Podolsky's model and when concentrating on the antighost number zero part of
the master action after deformation process, we get the non-Abelian extensions
of the Podolsky's theory. Furthermore, we calculate the number of physical
degrees of freedom in the resulting higher derivative system utilizing
Dirac-Bergmann algorithm method and show that it is unchanged if the consistent
interactions are included into the free theory.
