A kind of planar network of strings with non-collocated terms in
boundary feedback controls is considered. Suppose that the network
is constituted by $n$ non-uniform strings, connected by one
vibrating point mass. The displacements of these strings are
continuous at the common vertex. The non-collocated terms are
contained in feedback controls at
exterior nodes. The well-posedness of the corresponding closed-loop system is
proved. A complete spectral analysis is carried out and the
asymptotic expression of the spectrum of this system operator is
obtained, which implies that the asymptotic behavior of the spectrum
is independent of these non-collocated terms. Then the Riesz basis
property of the (generalized) eigenvectors of the system operator is
proved. Thus, the spectrum determined growth condition holds.
Finally, the exponential stability of a special case of this kind of
network is gotten under certain conditions. In order to support
these results, a numerical simulation is given.