In this paper, we consider the precoder design for downlink multiple-input multiple-output (MIMO) rate-splitting multiple access (RSMA) systems. The proposed scheme with simultaneous diagonalization (SD) decomposes the MIMO channel matrices of the users into scalar channels via higher-order generalized singular value decomposition for the common message (CM) and block diagonalization (BD) for the private messages, thereby enabling low-complexity element-by-element successive interference cancellation (SIC) and decoding at the receivers. Furthermore, the proposed SD MIMO-RSMA overcomes a critical limitation in RSMA systems, whereby the achievable rate of the CM is restricted by the users with weak effective MIMO channel for the CM, by excluding a subset of users from decoding the CM. We formulate a non-convex weighted sum rate (WSR) optimization problem for SD MIMO-RSMA and solve it via successive convex approximation to obtain a locally optimal solution. Our simulation results reveal that, for both perfect and imperfect CSI, the proposed SD MIMO-RSMA with user exclusion outperforms baseline MIMO-RSMA schemes and linear BD precoding.