Exponential stability of one class on nonlinear stochastic systems

Frequency conditions are obtained for exponential stability of one-dimensional nonlinear systems of Lurie type with a continuous time sand disturbed by multiplicative noises. With these conditions met the variance of phase coordinates decreases in time at least as fast as the exponential function of power known in advance. For the case of systems also subjected to additive noises frequency conditions for ergodicity and an estimate of the value of the quadratic performance functional are obtained.