Sound pressure radiating from vibrating structures submerged in fluid, as in the case of a vibrating panel in a submarine hull, is usually undesirable. An optimal control methodology for the suppression of far-field acoustic radiation pressure from submerged structures has been developed by Meirovitch (ref. 1). The linear modal state feedback control law developed implies that the full state (displacements and velocities) is available, perhaps through measurements. However, in practice, it is not always feasible to measure the full modal state vector for feedback. To permit practical implementation of the feedback control law, an optimal stochastic state estimator, or Kalman-Bucy filter, has been developed here for incorporation into the control system design. The development has been specialized to a uniform simply supported rectangular plate. / Master of Science