Robust Stability of Networks of iISS Systems: Construction of Sum-Type Lyapunov Functions
Robust Stability of Networks of iISS Systems: Construction of Sum-Type Lyapunov Functions
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DOI：
10.1109/tac.2012.2231552
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发表时间：
2013-05
影响因子：
6.8
通讯作者：
H. Ito;Zhong-Ping Jiang;S. Dashkovskiy;Björn S. Rüffer
中科院分区：
文献类型：
--
作者：
H. Ito;Zhong-Ping Jiang;S. Dashkovskiy;Björn S. Rüffer
本文给出了由积分输入-状态稳定（iISS）子系统组成的网络的稳定性检验问题的一种解决方法。最近发展的iISS小增益定理已被限制到两个子系统的互连。对于大规模系统，之前开发的仅依赖于增益类型信息的稳定性标准仅针对输入到状态稳定（ISS）子系统。为了解决在一般结构中互联的iISS子系统的稳定性问题，本文展示了如何通过在适当的小增益条件下的子系统的非线性重新标度的个体Lyapunov函数的总和来构造网络的Lyapunov函数。
This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnections of two subsystems. For large-scale systems, stability criteria relying only on gain-type information that were previously developed address only input-to-state stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled individual Lyapunov functions of subsystems under an appropriate small-gain condition.