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The stability analysis via the Lyapunov theorem for Autonomous Ratio-Memory Cellular Nonlinear Networks (ARMCNNs) is proposed. A conservative domain of attraction (DOA) is found from the stability analysis through a graphical method without complicated numerical analysis. The stability analysis shows that ARMCNNs can tolerate large ratio weight variations. This paper also presents the ARMCNN with self-feedback (SARMCNN) to overcome the problem of isolated neurons due to low correlation between neighboring neurons. The SARMCNN recognition rate (RR) is compared with other CNN constructed via the singular value decomposition technique (SVD-CNN).