ИСТИНА

The paper uses a variational approach to study the optimization and stability of one essentially nonlinear dynamic system.(see [1]) For many essentially nonlinear dynamical systems, (adequate) stability and optimization methods have not yet been developed. This is due to the fact that the classical Lyapunov method is not always applicable, even in those cases when the Lyapunov function is constructed. However, the implementation of the Lyapunov method poses difficulties of both a qualitative and a quantitative nature in studies of this dynamic system for stability. In such cases, it is more convenient to apply the variational approach to the study of stability. It allows you to fairly accurately establish the necessary stability conditions for a substantially nonlinear system. The proposed method (see [2]) is based on a variational method for estimating the rate of change of the metric of the phase space of states of a perturbed system. The authors congratulate dear Shavkat Arifdzhanovich Alimov on his anniversary and wish him health and success in his scientific work.