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This paper presents a stochastic state feedback \(\mathcal{L}{}_{1}\) adaptive control for systems with matched disturbances. The proposed approach is characterized through the introduction of a Kalman type fixed gain in the predictor. The main contribution of this work is that closed loop system analysis is demonstrated through a deterministic-like approach that uses the stochastic Laplace transform. The control is designed to accommodate and to be robust to unknown input gain as well as to system uncertainties. Simulation results show good results for the pitch angle control of a small fixed wing UAV.