  For topological characterization of non-Hermitian multiband systems,
Majorana's stellar representation (MSR) is applied to 1D multiband models
consisting of asymmetric nearest-neighbor hopping and imaginary on-site
potentials. The number of edge states isolated from the continuous bulk bands
in the complex energy plane is successfully linked with a topological invariant
constructed from MSR. Specifically, the number of isolated edge states can be
obtained from a winding number defined for the Majorana stars, which also
allows for a geometric visualization of the topology related to the isolated
edge modes. A remarkable success of our approach is that our winding number
characterization remains valid even in the presence of exceptional points of
the continuous bulk bands, where the Hamiltonian becomes non-diagonalizable and
hence conventional topological invariants such as the Zak phase and the Chern
number cannot be properly defined. Furthermore, cases with the so-called
non-Hermitian skin effect are also studied, showing that the bulk-boundary
correspondence between our defined winding numbers and isolated edge states can
be restored. Of particular interest is a four-band example with an odd number
of isolated edge states, where the Zak phase approach necessarily fails upon
removing the skin effect, but our MSR-based characterization works equally
well. For these reasons, our study is expected to be widely useful in
topological studies of non-Hermitian multiband systems, regardless of the skin
effect or the presence of the exceptional points in non-Hermitian systems.
