Stochastic problems of absolute stability

Abstract

The publications concerned with the development of the theory of absolute stability of stochastic systems were reviewed. The criteria for absolute stochastic stability based on the V.A. Yakubovich frequency theorem and algebraic approaches which do not use the frequency theorem were presented. A stochastic analog of the frequency theorem was formulated, and its features were discussed. A relation between the problems of absolute stochastic stability and optimal stochastic control was established. The results on some problems of stochastic stabilization based on the frequency theorem were considered. Some criteria for stochastic stability of the pulse systems established on basis of the frequency theorem were presented. The problems of passivity and dissipativity of the nonlinear stochastic systems were discussed. The state-of-the-art of the theory was briefly characterized in conclusion.