This paper focuses on addressing the issue of absolute stability for uncertain Lur’e systems with time-varying delay using a delay-segmentation approach. The approach involves decomposing the delay interval into two distinct subintervals of unequal lengths. This allows for the introduction of a delay-segmentation-based augmented Lyapunov–Krasovskii functional that ensures piecewise continuity at the partition points. By selecting two sets of Lyapunov matrices for the time-varying delay in each interval, the obtained results are less conservative, providing a more accurate assessment of absolute stability. Finally, a numerical example is given to demonstrate the superiority of the delay-segmentation approach.

Brain tumors usually appear as masses formed by localized abnormal cell proliferation. Although complete removal of tumors is an ideal treatment goal, this process faces many challenges due to the aggressive nature of malignant tumors and the need to protect normal brain tissue. Therefore, early diagnosis is crucial to mitigate the harm posed by brain tumors. In this study, the classification accuracy is improved by improving the ResNet50 model. Specifically, the image is preprocessed and enhanced firstly, and the image is denoised by fractional calculus; then, transfer learning technology is adopted, the ECA attention mechanism is introduced, the convolutional layer in the residual block is optimized, and the multi-scale convolutional layer is fused. These optimization measures not only enhance the model’s ability to grasp the overall details but also improve its ability to recognize micro and macro features. This allows the model to understand data features more comprehensively and process image details more efficiently, thereby improving processing accuracy. In addition, the improved ResNet50 model is combined with EfficientNetB0 to further optimize performance and improve classification accuracy by utilizing EfficientNetB0’s efficient feature extraction capabilities through feature fusion. In this study, we used a brain tumor image dataset containing 5712 training images and 1311 validation images. The optimized ResNet50 model achieves a verification accuracy of 98.78%, which is 3.51% higher than the original model, and the Kappa value is also increased by 4.7%. At the same time, the lightweight design of the EfficientNetB0 improves performance while reducing uptime. These improvements can help diagnose brain tumors earlier and more accurately, thereby improving patient outcomes and survival rates.

This note proposes a novel weighted memory $H_\infty$ controller for time-varying delayed Takagi-Sugeno fuzzy systems via a distributed delay method. In contrast to the traditional memory controller based on instantaneous historical data, the continuous historical information over a given period is utilized to construct the fuzzy-based memory controller, in which a weighting function is employed for the first time to describe the importance of historical information. Then, the weighted historical information is expressed as a distributed delay and the weights are represented as delay kernel. By using a less conservative integral inequality with respect to the weighted historical information, original sufficient conditions are deduced to solve the fuzzy weighted memory $H_\infty$ controller gains. Lastly, simulations are carried out to reveal the merits of the presented controller.