The article deals with the author's experience of solving the problem of improving the quality of identification of complex objects by the recorded analog signals using recognition systems that implement the convergence of decision rules synthesized on the same samples using methodologically different approaches. The mathematical tools are considered: the statistical approach implemented by calculating the author's indicators of the system organization–analogues of statistical moments of the third and fourth orders; the synergetic approach-indicator latent variables are proposed to form on the basis of matrix transformations of the bi-spectral autocorrelation function of the recorded signal, the parameters of the time shift of which are adjusted in accordance with the Fourier spectrum of the reference classes of the objects. The results of testing the proposed methods on the example of solving a medical problem-preventive diagnosis of destructive lung conditions in asthmatic diseases are reduced. It is shown that the convergence of different rules allows to obtain identification solutions more correlated with independent external expertise than the results of their application separately.