This work presents the analytical design of a bilateral control algorithm based on state convergence, tailored for teleoperation systems with a submerged slave manipulator. Unlike conventional underwater teleoperation strategies that rely on heuristic or empirical tuning, the proposed method is grounded in state-space modeling and feedback linearization to compensate for gravitational and hydrodynamic forces. A novel gain structure is developed using convergence criteria and desired settling times for both master and error dynamics. The control architecture ensures autonomous and stable error dynamics through decoupling and guarantees synchronized motion and force feedback between the manipulators. This contributes to the development of predictable, robust behavior in underwater tasks such as exploration, structural inspection, and object retrieval. The method lays the groundwork for experimental implementation and can be extended to real-time systems. Preliminary simulation results demonstrate stable tracking performance under varying dynamic conditions and model uncertainties.