Importance The paper studies the problems of organization of research of the sustainability of economic systems by analyzing their dynamic properties and investigating the potential of improvement of economic and mathematical modeling of such research. Objectives The study aims to formulate strategic ways to improve economic and mathematical modeling in order to dramatically improve the efficiency of research of economic dynamics of macro-systems based on dynamic input-output models, investigate the possibility of obtaining the base "input-output" tables for the administrative and economic regions, develop a conceptual model of control of the economic sub-motions as well as options for formalized control of the economic dynamics. Methods For the study, we used the input-output methods, theory of differential equations, methods of linear algebra, and the methods of applied nonlinear programming. Results The paper proposes a method of direct control of matrix eigenvalues of the dynamic model of interindustry balance, and justifies an algorithm to measure the degree of economic growth. Conclusions and Relevance We conclude that in modern Russia, management of dynamics and economic growth, as well as changing its structure are possible only on the basis of Keynesian methodology. The study's results are intended to be used by individuals and entities that make economic decisions both at the regional and country levels.
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