Dovhun A. The method of Lyapunov-Krasnovskii functionals research of stability of stochastic dynamical systems of automatic control with aftereffect considering Markov perturbations

The thesis is dedicated to investigation of stability of stochastic dynamical systems of automatic control in the presence of diffusion, impulse and Markov perturbations. Theorems considering existence and uniqueness of a strong solution of stochastic functional differential equations system with Poisson perturbations in the presence of random contactors are proved. Sufficient conditions for absolute stability in the mean quadratic of stochastic dynamic systems with nonlinear inverse link are outlined. For the first time sufficient conditions for absolute in nonlinearity and delay stability in the mean of quadratic systems of stochastic Ito-Skorokhod differential-difference equations are obtained in the present thesis. The problem of Kalman-Bucy filter construction for linear stochastic dynamic equations using discrete approximation of generalized Riccati equation is solved. At the same time, model problems are introduced: the asymptotic stability in mean quadratic of autonomous linear differential-difference systems with Markov parameters; the nonlinearity absolute asymptotic stability in the mean quadratic trivial solution of Ito-Skorokhod stochastic differential equation; the absolute in nonlinearity and delay asymptotic stability in the mean quadratic stochastic differential-difference equations with Poisson perturbations.