Optimization of a linear dynamic system with periodic changing parameters

The article deals with the problem of optimal control of a linear dynamic system with periodic parameters. The qualitative theory of such problems is developed very fully if the period of coefficients of the system is not very small. With a small period, there are serious difficulties with integration. Therefore, it is reasonable to supplement the constructive methods of solution with asymptotic ones. The article presents such an approach that the method of averaging is used to construct an auxiliary (basic) problem, estimates of the proximity of solutions to the initial and basic problems are obtained.