  This short note presents a summary of the articles arXiv:1408.5357,
arXiv:1412.5939, arXiv:1603.06796, arXiv:1606.01018, arXiv:1606.08148 that were
done in collaboration with N. CRAMPE, M. EVANS, C. FINN, K. MALLICK and M.
VANICAT. It presents an approach to the matrix ansatz of out-of-equilibrium
systems with boundaries, within the framework of integrable systems, and was
presented at ISQS24 (Prague, 2016).
