Minimal realization of completely decidable linear differential systems of observation

The equations in total differentials (Pfaff systems, multidimensional differential equations) are a specific class of partial differential equations with decidability being possible only under rather strict conditions. For a linear system S in total differential, a procedure is suggested for construction of its minimum realization S0. The S0 is such Pfaff vector equation when the phase domain has least dimensionality under the condition that the set of its output functions coincides with the output family of system S.