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In this paper, a new approach to solving a problem of steganography algorithm stability to cover-attack is proposed. The algorithm is based on the general approach to analysis of state and functioning of information system which was previously developed by the author. Consequently, we obtain the sufficient conditions for low-sensitivity of stegano message to compression while ensuring the reliability of perception. The proposed approach automates the process of analyzing the existing or emerging steganography algorithms from viewpoint of its resistance to compression. This became possible due to estimation of singular values perturbation of cover's matrix during the stegano transformation process. Additionally the proposed algorithm allows a priori selection of less sensitive to compression stegano messages from their variety. [ABSTRACT FROM AUTHOR]