Based on the concept of sliding mode control, we study the problem of steady state covariance assignment for bilinear stochastic systems. We find that the invariance property of sliding mode control ensures nullity of the matched bilinear term in the system on the sliding mode. By suitably using Ito calculus, the controller u(t) can be designed to force the feedback gain matrix G to achieve the goal of steady state covariance assignment. We also compare our method with other approaches via simulations.

Based on the concept of sliding mode control, this paper investigates the upper bound covariance assignment with H∞ norm and variance constrained problem for bilinear stochastic systems. We find that the invariance property of sliding mode control ensures nullity of the matched bilinear term in the system on the sliding mode. Moreover, using the upper bound covariance control approach and combining the sliding phase and hitting phase of the system design, we will derive the control feedback gain matrix G, which is essential to the controller u(t) design, to achieve the performance requirements. Finally, a numerical example is given to illustrate the control effect of the proposed method.