Stability of discrete systems with a random structure and in face of continuous disturbances

Discrete nonlinear stationary control systems are considered that are subjected to additive and parameteric Gaussian disturbances. The system structure is random and varies with the evolution of a stationary Markov chain with a stochastic matrix known. A theorem on stability of such systems is formulated and proved in face of continuous disturbances at the input; the theorem is applied to solution of the problem of optimal stabilization in a linear system and to analysis of a Lur'ye nonlinear system with the structure of these systems random. An example is given.