  The band structure of some translationally invariant lattice Hamiltonians
contains strictly dispersionless flatbands(FB). These are induced by
destructive interference, and typically host compact localized eigenstates
(CLS) which occupy a finite number $U$ of unit cells. FBs are important due to
macroscopic degeneracy and consequently due to their high sensitivity and
strong response to different types of weak perturbations. We use a recently
introduced classification of FB networks based on CLS properties, and extend
the FB Hamiltonian generator introduced in Phys. Rev. B 95, 115135 (2017) to an
arbitrary number $\nu$ of bands in the band structure, and arbitrary size $U$
of a CLS. The FB Hamiltonian is a solution to equations that we identify with
an inverse eigenvalue problem. These can be solved only numerically in general.
By imposing additional constraints, e.g. a chiral symmetry, we are able to find
analytical solutions to the inverse eigenvalue problem.
