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This paper provides estimation and control design methods for linear discrete-time systems with multiplicative noise. First, we present the design of the state feedback controller, such that the closed loop system is mean square stable. Second, we provide sufficient conditions for the existence of the state estimator; these conditions are expressed in terms of linear matrix inequalities (LMIs), and the parametrization of all admissible solutions is addressed. Finally, an estimator design approach is formulated using LMIs, and the performance of the estimator is examined by means of numerical examples.