Kuzmych E. The stability of logic-dynamical system with time switching.

This Thesis is dedicated to the important problems of the applied mathematics; specifically, to the development of methods for researching the dynamics of processes designed for the aggregate of differential and difference equations with logical laws of switching. The key property of the research focuses on the stability of systems which are important for planning the control systems. In the Thesis estimates of solutions for the logic-dynamical system with time switching are obtained. Such logic dynamical systems with time consist of subsystems. These subsystems are described by simpler systems of linear differential equations with constant coefficients and discrete equations. The estimates of the solutions for the logic-dynamical system are obtained. These systems consist of subsystems which are described by the systems of linear differential equations with delay, and discrete equations with delay. The estimates of solutions for the systems of equations of neutral type are also obtained. The model ofthe transport system of magnetic levitation is developed based on the example of the model of body motion with three degrees of freedom. The estimation of its solution is obtained by the analytical method, as well as by using the numeral experiment. The results, obtained during numerical experiments of the developed system, confirm the theoretical result of the linear systems.