This study investigates a robust reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) system for secure wireless communication, in which a multi-antenna transmitter (Alice) sends confidential messages to a multi-antenna receiver (Bob) in the presence of an eavesdropper (Eve). Unlike idealized models, the reflecting elements (REs) of the RIS are assumed to possess inherent electrical resistance, introducing a practical non-ideal effect often neglected in prior research. The aim of the study is to maximize the secrecy rate of the MIMO system under perfect knowledge of the channel state information (CSI). To achieve this, the secrecy rate maximization problem is formulated and solved using a low-complexity joint optimization framework based on an adaptive projected gradient method (PGM), which simultaneously updates both the transmit precoding matrix and the RIS phase shifts. Solving the exact problem is computationally complex. Thus, a simplified variant is further introduced that maximizes the channel power difference rather than the exact secrecy rate. The simulation results show that this approximation yields a secrecy rate close to the true optimum while significantly reducing the computational cost. In addition, the proposed PGM with an adaptive step size initialization and control mechanism substantially improves the secrecy rate and reduces the computational time compared to the conventional fixed step size PGM. Overall, the simulation results confirm the effectiveness of the proposed PGM and demonstrate that adopting a practical RIS model is essential for establishing secure RIS-assisted MIMO communication links, especially under varying RE resistance values.