Based on the concept of variable structure control, this paper investigates the steady state covariance assignment problem for perturbed stochastic multivariable systems. By using the invariance property of variable structure systems, the matched perturbation of the system disappears on the sliding mode. With the aid of Ito-formula, the controller u(t) is proposed. Combining the sliding phase and hitting phase of the system design, the control feedback gain matrix G is derived to satisfy the steady state covariance assignment. (C) 1999 Elsevier Science B.V. All rights reserved.