On the stability of stochastic Lur´e systems with differentiable nonlinearity

The method of Popov is extended in the paper in order to derive sufficient conditions for the asymptotic stability in the mean of a Lur´e-type nonlinear feedback system having stochastic parameters in the linear part. It is assumed that the nonlinear characteristic is specified by known bounds on the slope, as well as on the sector in which it may lie. It is also assumed that the statistics of the random parameters of the linear subsystem are known. The stability conditions developed are analogous to those proved for the deterministic versions of the problem.