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This paper focuses on the reachable set problem for impulse switched singular (ISS) systems with mixed time-varying delays via the Lyapunov theory. To solve the state boundary of system, a real-bounded lemma is developed by analyzing the impulse switching point under bounded disturbance input and initial function. Based on real-bounded lemma and integral inequality technology, a sufficient condition for reachable set of ISS system is established in the form of linear matrix inequalities (LMIs) to ensure that the reachable state of system is limited to a closed bounded set. Simulation results are given to verify the validity of the obtained theoretical results for the reachable state criterion.

Most of the shape classification methods are based on a single closed contour. However, practical shapes always have complex contours, for example, a combination of multiple open contours. How to accurately identify complex shapes is an unsolved problem. In this research, a novel method is proposed to classify complex shapes. The proposed method firstly encodes a complex shape to an angle code and a sparsity code, then input these codes to a 1-D CNN for extracting features and classification. Experiments on two datasets show this novel method is superior in terms of classification accuracy. These two datasets are practical shape dataset collected by this paper on internet and MPEG-7 CE-1 Part B. The proposed method achieves higher classification accuracy than compared methods. In order to show the performance of the proposed method on each class, the accuracy on each class is analyzed. Ablation experiment is conducted to show the contribution of each module in the network. The result shows that each module is meaningful in the network, because without any module the accuracy drops.

In the post-epidemic era, along with the continuous upgrading of Internet technology, the live-streaming with goods industry is booming. This new shopping method has attracted consumers, deeply integrated into people's daily lives and has a bright future for development. This study is based on a questionnaire and data analysis using LIWC and Excel to analyze three aspects of emotional motivation (sense of belonging, respect, and self-actualization) that influence consumers' purchase behavior in live rooms. Research shows that emotional motivation is an important factor influencing consumers' purchasing behavior. Purchase behavior is positively correlated with the sense of belonging, respect, and self-actualization. Meanwhile, the sense of belonging has the most significant influence, followed by the sense of respect and, finally, the sense of self-actualization. This study can help practitioners of live banding understand consumers' emotional needs, improve sales strategies and enhance competitiveness. At the same time, it is beneficial for consumers to understand the emotional motivation of their shopping behavior, shape the correct consumption concept, make scientific decisions, identify undesirable shopping guide behavior and avoid entering consumption misconceptions.