Intelligent reflecting surface (IRS) has recently emerged as a promising technology for 6G wireless systems, due to its capability to reconfigure the wireless propagation environment. In this paper, we investigate a Rate-Splitting Multiple Access (RSMA) for IRS-assisted downlink system, where the base station (BS) communicates with single-antenna users with the help of an IRS. RSMA relies on rate-splitting (RS) at the BS and successive interference cancellation (SIC) at the users and provides a generalized multiple access framework. We derive a new architecture called IRS-RS that leverages the interplay between RS and IRS. For performance analysis, we utilize an \textit{on-off control technique} to control the passive beamforming vector of the IRS-RS and derive the closed-form expressions for outage probability of cell-edge users and near users. Moreover, we also analyze the outage behavior of cell-edge users for a sufficiently large number of reflecting elements. Additionally, we also analyze the outage performance of cooperative RS based decode-and-forward (DF)-assisted framework called DF-RS. Through simulation results, it is shown that the proposed framework outperforms the corresponding DF-RS, RS without IRS and IRS-assisted conventional non-orthogonal multiple access (NOMA) schemes. Furthermore, the impact of various system’s parameters such as the number of IRS reflecting elements and the number of users on the system performance is revealed.