The analysis of existent approaches of mathematical design of the technical systems is conducted in the article. The mathematical model of the computer system of critical application (KSСА), different from known the account of factor of a priori vagueness of external destructive influences, is developed. Researches of adequacy of the developed model are conducted in the conditions of possible ill-intentioned influence. The phase portraits of KSСА, functioning in normal and anomalous terms are built.
computer system of critical application, external ill-intentioned influences, space of problems, phase portrait