In the paper, a complete proof of the properness and mean-square exponential stability for stochastic Brownian systems is firstly addressed, which lays a solid foundation for system analysis and control synthesis for this kind of stochastic systems. Observer-based controller for the descriptor system with Brownian motions is then investigated. It is noticed that the system dynamics and observer dynamics are both subjected to state Brownian fluctuation, which makes it challenging either to design observer gain and controller gain simultaneously or design the observer and control gains by using a complete separation design technique. A sequential design technique is proposed to calculate the control and observer gains by solving linear matrix inequalities. The proposed design methods are readily extended to the case for stochastic descriptor systems with multiple Brownian motions. A numerical example is finally given to illustrate the design techniques, and simulated results have demonstrated the efficiency.