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Output-feedback (observer-based) robust and optimal control law which guaranteesglobal (local) asymptotic stability in probability for nonlinear stochastic dynamicsystem are stated, developed and proved with the help of stochastic Lyapunov functionapproach supported by necessary theorems and an illustrative example. The inverseoptimal stabilization in probability with suitable performance index has also beenstated and developed.

Backstepping --- control Lyapunov functions --- inverse optimality --- stochastic nonlinear output-feedback systems --- stochastic stabilization.