  This paper performs a stability analysis of a class of moment closure systems
derived with an extended quadrature method of moments (EQMOM) for the
one-dimensional BGK equation. The class is characterized with a kernel
function. A sufficient condition on the kernel is identified for the
EQMOM-derived moment systems to be strictly hyperbolic. We also investigate the
realizability of the moment method. Moreover, sufficient and necessary
conditions are established for the two-node systems to be well-defined and
strictly hyperbolic, and to preserve the dissipation property of the kinetic
equation.
