Stochastic differential equations are one of the most useful areas of the theory of stochastic processes and its applications in mathematics Some nonlinear (Itô) 1 dynamic stochastic control system driven by Brownian motion 2 based on dynamic observer have been considered. Output feedback (observer – based) robust and optimal control law which guarantees global (local) asymptotic stable in probability for the nonlinear stochastic dynamic system are discuss and developed. The necessary theorems regarding the globalty asymptotic stable in the probability of the equilibrium point at the origin of the closed loop stochastic system have been developed and proved. The Lyapunov function approach of stochastic dynamic system has been adapted to justify our proofs. The inverse optimal stabilization in probability with suitable performance index has also discussed and developed. The necessary mathematical requirements have also been provided. Concluding remarks, future work, computational algorithm based on the theoretical results and illustrations have been presented.