Construction of ISS Lyapunov functions for infinite networks of ISS systems

被引：0
|
作者：
Kawan, Christoph [1 ]
Mironchenko, Andrii [2 ]
Zamani, Majid [1 ,3 ]
机构：
[1] Ludwig Maximilians Univ Munchen, Inst Informat, D-80538 Munich, Germany
[2] Univ Passau, Fac Comp Sci & Math, D-94032 Passau, Germany
[3] Univ Colorado, Comp Sci Dept, Boulder, CO 80309 USA
来源：
2021 60TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC) | 2021年
基金：
欧盟地平线“2020”;
关键词：
large-scale systems; small-gain theorems; input-to-state stability; nonlinear systems; infinite-dimensional systems; SMALL-GAIN THEOREM; DISTRIBUTED CONTROL; STATE STABILITY; INPUT;
D O I：
10.1109/CDC45484.2021.9683184
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We show that an infinite network of input-to-state stable (ISS) systems, admitting ISS Lyapunov functions, itself admits an ISS Lyapunov function, provided that the couplings of the subsystems are sufficiently weak. The strength of the couplings is described in terms of the properties of the so-called gain operator, built from the interconnection gains. If the discrete-time system induced by a slightly scaled gain operator is uniformly globally asymptotically stable, an ISS Lyapunov function for the infinite network can be constructed.
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页码：4811 / 4816
页数：6
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