In this paper, we investigate the global stability of quaternion-valued neural networks (QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativity of quaternion multiplication, the QVNN is decomposed into four real-valued systems based on Hamilton rules: $ij=-ji=k,~jk=-kj=i$ , $ki=-ik=j$ , $i^{2}=j^{2}=k^{2}=ijk=-1$ . With the Lyapunov function method, some criteria are, respectively, presented to ensure the global $\mu $ -stability and power stability of the delayed QVNN. On the other hand, by considering the noncommutativity of quaternion multiplication and time-varying delays, the QVNN is investigated directly by the techniques of the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) where quaternion self-conjugate matrices and quaternion positive definite matrices are used. Some new sufficient conditions in the form of quaternion-valued LMI are, respectively, established for the global $\mu $ -stability and exponential stability of the considered QVNN. Besides, some assumptions are presented for the two different methods, which can help to choose quaternion-valued activation functions. Finally, two numerical examples are given to show the feasibility and the effectiveness of the main results.

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Background The practical application of the Canadian Agility and Movement Skill Assessment (CAMSA) has been reported in some Western countries. However, a few studies reported the application of the CAMSA in Chinese children. In addition, given that the CAMSA was designing to incorporate both movement skills and agility assessment, the value and validity of the timing component of the CAMSA are worth discussing. Methods By choosing the Illinois Agility Test, Repeated Side Step-1 m distance, and the newly designed Repeated Side Step-half of height as the benchmark, we evaluate the performance of the CAMSA, further establish the concurrent validity of the CAMSA timing components (completion time and time score). In total, 149 male children (mean age 9.0 ± 0.8 years) from public schools in Shanghai, China, participated in the study. Results The mean CAMSA completion time was 19.3 ± 5.3 (s), and mean time score was 8.7 ± 3.9 (range of 1–14) for all participants (n = 149). After adjusted the sprint speed, older age was positively associated with the performance of the CAMSA. Being overweight was not associated with the performance of the CAMSA comparing with healthy body mass children, however, being obese was negatively associated with the CAMSA timing components and total score. Children having extracurricular sports activities (e.g., athletic experiences), mostly soccer, were more likely to demonstrated better performances of the CAMSA completion time, time score and total score. However, overweight and obese, also athletic experiences were not significantly contributed to the CAMSA skill score, although the association was slight (Adj R2 = 0.13). Besides, the CAMSA completion time has a strong correlation with the IAT, r = 0.77; RSS-1MD, r =  − 0.76; and RSS-HHD, r =  − 0.77, p < 0.01. The same pattern of correlation was also found between the CAMSA time score and three agility tests: IAT, r =  − 0.79; RSS-1MD, r = 0.76; RSS-HHD, r = 0.78, p < 0.01. Discussion Overall, a few participants in the study were able to reach the recommended level of the total CAMSA score referring to the Canadian criterion. The strong concurrent validity was found between the CAMSA timing components and three selected agility tests, respectively.

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