论文标题
无限网络的轻松的小生命定理
A relaxed small-gain theorem for infinite networks
论文作者
论文摘要
在大型网络中的可伸缩性问题中，我们研究了无限许多有限维基系统网络的稳定性。我们开发了一个所谓的放松的小增生定理，以实现封闭式集合，以实现投入到国家的稳定性（ISS），并表明每个指数输入到国家稳定的系统都必须满足所提出的小增益条件。按照自下而上的方法，我们根据各个子系统的行为来研究互连的辅助性。最后，我们通过无限网络过度陈列的大而限制的网络，并表明，如果无限网络的每个子系统均为ISS，则可以将所有稳定性属性和无限系统获得的性能指数转移到原始有限的一个。有趣的是，不需要知道截断网络的大小。通过应用于城市交通网络，我们的小生命定理的有效性得到了验证。
Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a closed set and show that every exponentially input-to-state stable system necessarily satisfies the proposed small-gain condition. Following our bottom-up approach, we study the well-posedness of the interconnection based on the behavior of the individual subsystems. Finally, we over-approximate large-but-finite networks by infinite networks and show that all the stability properties and the performance indices obtained for the infinite system can be transferred to the original finite one if each subsystem of the infinite network is individually ISS. Interestingly, the size of the truncated network does not need to be known. The effectiveness of our small-gain theorem is verified by application to an urban traffic network.
