2023/12/12 by Jiamin Wang, Jian Liu, Yuanshi Zheng +1 · 1 citation
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #Neural Networks Stability and Synchronization #Advanced Memory and Neural Computing
paper · doi:10.1109/tac.2023.3342060
In this paper, we analyze the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">H∞ </tex-math></inline-formula> performance of the first-order continuous-time multi-agent consensus network and that of the corresponding sampled-data network in the presence of external disturbances. Firstly, we build the quantitative relation between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">H∞ </tex-math></inline-formula> performance and the eigenvalues of directed graph Laplacian for the continuous-time multi-agent network. Secondly, we establish the analytic expression of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">H∞ </tex-math></inline-formula> performance for the sampled-data multi-agent network, which depends not only the eigenvalues of Laplacian matrix but also the sampling period. It is proved that there exists a unique optimal sampling period such that the sampled-data multi-agent network obtains the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">H∞ </tex-math></inline-formula> performance. Furthermore, we show that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">H∞ </tex-math></inline-formula> performance of the sampled-data multi-agent network is not better than that of the original continuous-time multi-agent network. Finally, numerical tests are given on several well-known graphs.