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Multirate (MR) partitioning is emerging as a promising technique for improving the performance of complex power systems with limited computing resources. However, the modeling and stability evaluation methods of such MR power systems have not been fully investigated, which limits their wider application. An iteratively-nested state-space (INSS) modeling method is proposed in this article to improve the stability analysis accuracy of the MR power system. System partitions, with different discrete time-steps, are modeled in state-space and iteratively-nested with each other to form a single-rate system, the stability of which can then be evaluated with high accuracy based on the eigenvalue analysis. The technique of fractional sum of the power matrix is adopted for derivation when the discrete time-steps of the MR system are not integer multiples of each other. The modeling accuracy of the proposed method is higher than that of the linear averaging-based solution, while the modeling complexity is also greatly reduced compared with that of the lifting-based solution. A case study of a triple-rated power hardware-in-the-loop (PHIL) system is performed as an example to demonstrate the utility of the proposed INSS modeling method. Moreover, the presented modeling process is in a generalized form, and can be easily applied to the modeling and optimization of MR real-time simulation, MR digital-twin deployment, and MR process control for its engineering feasibility.