SIMPLE STABILITY-CRITERION FOR NONLINEAR-SYSTEMS WITH MULTIPLICATIVE NOISE

A new sufficient condition for mean square stability of stochastic systems with sector-bounded non-linearity is presented. Verification of modern stability criteria for systems under consideration is a complicated numerical problem. As a rule, in the process of verification of most of these criteria, we repeatedly have to solve non-linear matrix equations. We have used estimates of the solution of this equation and non-traditional matrix calculus. As a result, we obtained a simple, easy-to-check mean-square stability criterion.