  We introduce the notion of Gepner type Bridgeland stability conditions on
triangulated categories, which depends on a choice of an autoequivalence and a
complex number. We conjecture the existence of Gepner type stability conditions
on the triangulated categories of graded matrix factorizations of weighted
homogeneous polynomials. Such a stability condition may give a natural
stability condition for Landau-Ginzburg B-branes, and correspond to the Gepner
point of the stringy Kahler moduli space of a quintic 3-fold. The main result
is to show our conjecture when the variety defined by the weighted homogeneous
polynomial is a complete intersection of hyperplanes in a Calabi-Yau manifold
with dimension less than or equal to two.
