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Reconfigurable intelligent surfaces (RISs) have emerged as a prospective technology for next-generation wireless networks due to their potential in coverage and capacity enhancement. Previous works on achievable rate analysis of RIS-assisted communication systems have mainly focused on the rich-scattering environment where Rayleigh and Rician channel models can be applied. This work studies the ergodic achievable rate of RIS-assisted multiple-input multiple-output communication systems in millimeter-wave band with limited scattering under the Saleh-Valenzuela channel model. Firstly, we derive an upper bound of the ergodic achievable rate by means of majorization theory and Jensen's inequality. The upper bound shows that the ergodic achievable rate increases logarithmically with the number of antennas at the base station (BS) and user, the number of the reflection units at the RIS, and the eigenvalues of the steering matrices associated with the BS, user and RIS. Then, we aim to maximize the ergodic achievable rate by jointly optimizing the transmit covariance matrix at the BS and the reflection coefficients at the RIS. Specifically, the transmit covariance matrix is optimized by the water-filling algorithm and the reflection coefficients are optimized using the Riemannian conjugate gradient algorithm. Simulation results validate the effectiveness of the proposed optimization algorithms.