Doroshenko I. The stability of dynamic systems with afteraction of stochastic structurein view of Markov changeovers

The thesis is dedicated to study of stability and estimations on the average quadratic of solutions of Stochastic Differential Equations of Neutral Type with Poisson Changeovers (NSDE with PC). In the dissertation the theorem of the existence and uniqueness of the solutions of NSDE with PC is obtained. Through the second Lyapunov method the sufficient conditions of asymptotic stability on the average quadratic of such equations solutions are derived. Through the obtained results the sufficient stability conditions for linear NSDE with PC and few time deviations are employed. For solutions of linear NSDE with PC the conditions and estimations on the average quadratic stability and exponential stability on the average quadratic are established. The example about applications above results to stochastic model of electrical networks containing lossless transmission lines is given. The results have an algebraic structure and may be employed in study of physical, biological, sociologic, economic process, which describes ground of NSDE.