This paper presents the contribution of a matrix converter for frequency stabilization for an energy source. Venturini optimal amplitude method is used. The energy source frequency is assumed to be purely random. A new approach based on the concept of Lyapunov's functions is revealed. The study is done for an electrical network with a random variable frequency, following the normal distribution and a typical RL load. The approach is tested using simulations under MATLAB® /Simulink® environment. The criteria used in the analysis are signal form, frequency analysis, and THD. The performances obtained are discussed.