On stability of systems of differential equations with stochastic structural changes (Q1589159)

A system of stochastic structure with finite number of states is considered. In each structural state, the system is described by an ordinary vector differential equation, and the process of change of structural states is represented by a homogeneous Markov chain with given transition probabilities. The Lyapunov techniques are used to solve the problem of asymptotic mean square stability of the solution \(x=0\). An example of a linear system with two structural states is given.