Stability of linear multi-dimensional stochastic systems with white noise

A new algebraical stability criterion is suggested for linear systems subjected to parametric disturbance by white noise. The knowledge of the dynamic responses of the deterministic part of the system and of static responses of the noises is used for construction of a certain linear finite-dimensional operator whose spectrum characterizes stability. A comparison with the well-known method [1] is made. Cases of describing the system by stochastic integral or differential equations. The results are given for the nonstationary case or for the case of differential equations. An example is given.