Constructing the lyapunov functions for linear systems with random coefficients

The stability of solutions of linear systems is studied with the use of Lyapunov functions. The work is aimed at deriving equations defining the Lyapunov functions for linear differential and difference equations with random Markov and semi-Markov random coefficients, development of methods of their solution. It is shown that the conditions of existence of the Lyapunov functions for nonstationary systems are equivalent to sigma -stability of solutions; necessary and sufficient conditions of existence of the Lyapunov functions with random Markov and semi-Markov coefficients are found, methods of construction thereof are developed. The results can be used for studying the stability of the control system motion under random actionsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio