В даній статті розглянуто проблему синтезу оптимальних за мінімальним значенням інтегрально-квадратичного критерію динамічних систем, які описуються моделлю рівнянь в змінних стану.
The dynamical systems given by integro-differentiation models with K-symmetric K-positive-definite operator are considered. The variational-gradient method was applied to those models. The analysis showed that the implementation of this method does not require knowledge of the operator spectrum, in addition, it has a better convergence rate and is more resistant to disturbances than gradient methods. The theorem is proved in this paper, which allows us to draw conclusions about the effectiveness of the application of the variational-gradient method for the research of c