Stability of singularly perturbed stochastic systems

Consideration is given to the rms stability of a linear singularly perturbed system of differential equations whose coefficients are perturbed by the Gaussian white noise. The theory of integral manifolds of determinate singularly perturbed systems is used to obtain the stability conditions. The effect of random forces on the stability of gyroscopic systems is discussed. The stability conditions are established. The possibility of replacing the complete equations of motion by the precession ones is considered, and a simple example shows that in the presence of the matrix of gyroscopic forces the precession equations can provide an erroneous result.