<p>This paper investigates the decentralized linear quadratic control problem for systems with observation and multiplicative noise. The system is controlled by two controllers, where the available information for the second controller involves the first controller. Multiplicative noise and observation arise simultaneously in the system model, which differs from the existing literature. The inapplicability of the separation principle and the highly nonlinear characteristics of the observation-based controller optimization problem make the search for the optimal solution quite difficult. The explicit output feedback controllers are designed based on the linear estimator using the matrix maximum principle. An iterative algorithm is presented to compute the gain matrices, and a sufficient condition is given for the mean-square stability of the system. Finally, a vehicle platoon problem is tackled with the acquired theoretical results.</p>