On control of systems delays in economics

The paper continues presentation of the differential game theory for systems with delays and is devoted to the solution of an approach problem in application to economic problems (Dockner E.J., et all, 2000; R. Isaacs, 1999). The results are obtained in the framework of the positional differential game theory (N.N. Krasovskii, A.I. Subbotin, 1988; A.V. Kryazhimskii, Yu.S. Osipov, 1973; Yu.S. Osipov, J. Appl. Math. Mech. Vol. 35, № 1, № 6, 1971) with application of the i-smooth analysis methodology (A.V. Kim, 2015). Effective construction of extremal positional control is based on the utilization of the so called u-stable sets The necessary and sufficient conditions of high u-stability are presented in the paper.