  We consider nxn hyperbolic systems of balance laws in one-space dimension
under the assumption that all negative (resp. positive) characteristics are
linearly degenerate. We prove the local exact one-sided boundary null
controllability of entropy solutions to this class of systems, which
generalizes the corresponding results from the case without source terms to
that with source terms. In order to apply the strategy used for conservation
law, we essentially modify the constructive method by introducing two different
kinds of approximate solutions to system in the forward sense and to the system
in the rightward (resp. leftward) sense, respectively, and we prove that their
limit solutions are equivalent to some extend.
