A lication of Lyapunov’s quadratic functions in solving a lied dynamic problems

In the following paper, we propose a technique for determining the moment of the end of the transient process when the parameters of a continuous dynamic system are changed on the basis of the application of the direct Lyapunov method, based on the estimation of the regions of attraction of equilibrium states. For an estimate of the region the trajectory of the system does not leave with time, we take a neighborhood of the equilibrium state where the first derivative of the Lyapunov function is negative. The Lyapunov function is chosen in the form of a positive definite quadratic form, where the negative sign of its first derivative is provided with a given margin due to a linear system.