Shusharin Y. Stability analysis and optimization of linear dynamic systems with Markov switching.

The thesis is devoted to the actual direction of the theory of linear difference and differential equations with random coefficients and random jumps. We study the stability of solutions for first and second moments, for which we deduce the moment equations, linear difference equations with coefficients that depend on two consecutive values of Markov chain, algebraic criteria for asymptotic stability of linear difference equations with random coefficients and stochastic Lyapunov functions for difference equations. In this paper we deduce moment equations for linear stochastic equations with random coefficients, we investigate the stability of solutions of non-stationary system of linear differential equations with random coefficients, the stability of zero solutions of equations for the moment functions of the first and second orders. We find the initial data optimum sets in mean values stability problems for difference equations with Markov coefficients and the initial values sets in integral moment stability for linear stochastic equations with continuous time.