The paper develops Lyapunov’s direct method on the basis of the concept of matrix-function (don’t confuse it with a scalar function in the vector-matrix notation). The equilibrium state stability of the above-mentioned systems is investigated both by the immediate application of matrix-function and by transfer to a scalar function. It is shown that the second level decomposition yields naturally the introduction of matrix-function with a subsequent construction of stability criteria in terms of the property of having fixed sign of suitable matrices in the cone. In the paper a two-component system is also considered.