Small gain theorems for large scale systems and construction of ISS Lyapunov functions

被引：0

作者：

Dashkovskiy, Sergey N. ^{[1
]}

Rueffer, Bjoern S. ^{[2
]}

Wirth, Fabian R. ^{[3
]}

机构：

[1] Univ Appl Sci Erfurt, Dept Civil Engn, Altonaer Str 25, D-99085 Erfurt, Germany

[2] Univ Paderborn, EIM E, Signal & Syst Theory Grp, D-33098 Paderborn, Germany

[3] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

来源：

2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC) | 2012年

关键词：

Nonlinear systems; input-to-state stability; interconnected systems; large scale systems; Lipschitz ISS Lyapunov function; small gain condition; TO-STATE STABILITY; FORMULATION;

D O I：

暂无

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 consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems.

引用

页码：4165 / 4170

页数：6

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