A new technique of data reconciliation, applied to validation of measures collected on a system, is suggested in this paper. This approach is based on the inequality constraints describing the hyper space in which the state of the considered system is probably located. We also use the model of the system in which the residuals must, in the same way, be constrained in an hyper space. Finally, the complete problem of reconciliation appears in the form of LMI (linear matrix inequality) and thus can be solved with the software tools that are appropriate to this technique. Some examples show that classical problems of balance equilibration can be solved: total Row balances, partial flow balances, balances with partial measures, consideration of biased measures.