STUDIES AND APPLICATIONS OF ABSOLUTE STABILITY OF THE NONLINEAR DYNAMICAL SYSTEMS

In this paper there are presented the methods of study for the automatic regulation of the absolute stability of the nonlinear dynamical systems. There are specified two methods for the absolute stability with the criteria and the type of application: a) the Lurie method with the effective determination of the Liapunov function; b) the frequencies method of the Romanian researcher V. M. Popov using the transfer function in the critical cases. The nonlinear dynamical systems reefers to the special classes include the linear and nonlinear blocks, due to the perturbations composed with the inverse actions of response of the automatic regulators components to obtain the stable absolute regime. The mathematical methodology is analytical numerically and the application used by the two methods is from the metal cutting tools machine and in the absolute stability of the rate of aircraft (airplane) equipped with autopilot.