In this article, based on Lyapunov–Krasovskii functional approach and improved delay-partitioning idea, a new sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic time-varying delay is addressed. Together with general convex combination method, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time delay range and its derivative, which has wider application fields than those present ones. It can be shown by the numerical examples that our method reduces the conservatism much more effectively than earlier reported ones. Especially, the conservatism can be further decreased by thinning the delay intervals.

Efficient anomaly detection is at the forefront of ensuring optimized operations and system safety, especially in the field of engineering. It is deemed indispensable for the enhancement of work efficiency, maximization of resource utilization, and proactive addressal of potential risks. From this practical perspective, a new method for granular representation of time series data is proposed in this study and is validated through a collective anomaly detection task. The density peak clustering (DPC) algorithm is employed to evaluate clusters in two-dimensional (2-D) data, which are created from the original dataset and its variations. Using the principle of justifiable granularity, each cluster is depicted, allowing the time series to be converted into rectangular information granules. A distinctive similarity measure, designed to assess the similarity among subsequences in this format, is then introduced, with subsequences having reduced similarity being pinpointed as anomalies. Extensive testing on various datasets confirms that the effectiveness and applicability of the proposed method are evident in real-world scenarios. This approach not only enhances the understanding of time series patterns but is also recognized for its prominence in engineering applications where precise anomaly detection is demanded. Due to its ability to capture the inherent structure of time series and analyze the correlation among data, superior effectiveness is consistently exhibited by the proposed approach when compared to other existing methods.

Different sensors may experience degeneracy in specific scenarios, which can lead to failures in multi-sensor fusion optimization. To address the challenges of localization and mapping under such degeneracy conditions, this paper proposes a LiDAR-Inertial-Visual SLAM system with integrated degeneracy awareness. In the frontend, the system utilizes the ESIKF for tracking and incorporates a sensor degeneracy detection method to ensure that degraded sensor data do not affect the state error update. In the backend, we replace the conventional point cloud map with an adaptive voxel map to accelerate the retrieval of planar point cloud, and merge LiDAR planar features within a sliding window via region growing algorithm. Furthermore, the point-to-plane distance formula is optimized via the Rayleigh quotient theorem, which reduces the dimensionality of the optimization variables and simplifies the optimization process. Finally, we evaluate the proposed system on several challenging datasets and compare it with various state-of-the-art sensor fusion systems. The experimental results demonstrate that the proposed system achieves high localization accuracy in the majority of challenging scenarios.