The detection and segmentation of infrared small targets have important application significance in the fields of surveillance and security, maritime rescue and so on. Due to the low occupancy of these targets in long-distance imaging, the mainstream visual state space model is inefficient and difficult to accurately model the target edge. The existing infrared state space models do not deviate from the mainstream visual state space structure framework from the structural properties of infrared small targets. In order to solve this problem, this paper proposes the RPCASSM network based on the model paradigm of robust principal component analysis(RPCA), which aims to design the background state space module(BSSM) and the target state space module(TSSM) by the nature of the infrared small target in the spatial domain. The BSSM aims to use the saliency of spatial heterogeneous signals to design a spatial probe scanning mechanism(SPCM) to model background information. The TSSM designs a deformable prompt scanning mechanism(DPCM) by using the sparsity and local highlight of the target to focus on the deformable space of the target for state space modeling. According to the above design, we effectively solve the problem that the existing mainstream vision state space model is difficult to accurately model the edge structure of infrared small target. Experimental results on the existing benchmark data sets prove the effectiveness of the RPCASSM design. Our code will be made public at \href{https://github.com/PepperCS/RPCASSM}{RPCASSM}.