  We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a
bounded smooth domain of $\mathbb{R}^{3}$ with a strictly positive conductivity
subject to the boundary conditions of a perfect conductor. Under appropriate
regularity conditions, adopting a classical $L^{2}$-Sobolev solution framework,
a nonlinear energy barrier estimate is established for local-in-time
$H^{3}$-solutions to the Maxwell system by a proper combination of higher-order
energy and observability-type estimates under a smallness assumption on the
initial data. Technical complications due to quasilinearity, anisotropy and the
lack of solenoidality, etc., are addressed. Finally, provided the initial data
are small, the barrier method is applied to prove that local solutions exist
globally and exhibit an exponential decay rate.
