查看更多>>摘要：A B S T R A C T The almost sure exponential stabilization and pth moment exponential stabilization for hybrid stochastic system (HSS) with control input delay, Levy noise and asynchronous switching will be studied in this paper. Adequate conditions will be built to ensure the pth moment stability for the HSS which refer to the sizes of the delays by taking full advantage of Lyapunov functional approach. We investigate the almost sure exponential stability standard of nominal systems by using compound Lyapunov function method with modal dependence. In addition, we further study the almost sure exponential stability for HSS with Levy noise and delayed feedback controller according to the comparison principle for sufficiently small delays as long as the nominal system is almost surely exponentially stable. An example and some simulations will propose to illustrate the results.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The anti-adjacency matrix (or eccentricity matrix) of a graph is obtained from its distance matrix by retaining for each row and each column only the largest distances. This matrix can be viewed as the opposite of the adjacency matrix, which is, on the contrary, obtained from the distance matrix of a graph by keeping for each row and each column only the distances being 1. In this paper, we prove that the graphs with exactly one positive anti-adjacency eigenvalue are determined by the anti-adjacency spectra. As corollaries, the well-known (generalized) friendship graphs and windmill graphs are shown to be determined by their anti-adjacency spectra.(C) 2022 Elsevier Inc. All rights reserved.
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