By using the describing function approximation method, the covariance control of a multivariable stochastic system with hysteresis nonlinearities is studied. Since the describing function for a hysteresis nonlinearity is always a complex form, this complex component in the system makes the problem more complicated. This paper proposes a condition under which the designed state feedback gain is guaranteed to be real and the specified state covariance X of the closed loop system is also achieved.
