Robust Stability of Networks of iISS Systems: Construction of Sum-Type Lyapunov Functions

Author

Ito, H. ; Jiang, Z.-P. ; Dashkovskiy, Sergey N. ; Ruffer, Bjorn S.

Author_Institution

Department of Systems Design and Informatics, Kyushu Institute of Technology, Iizuka, Fukuoka, Japan

Volume

58

Issue

5

fYear

2013

fDate

May-13

Firstpage

1192

Lastpage

1207

Abstract

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.

Keywords

Educational institutions; Gain; Lyapunov methods; Stability criteria; Trajectory; Vectors; Integral input-to-state stability (iISS); Lyapunov functions; large-scale systems; nonlinear systems; robust stability criteria;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2012.2231552

Filename

6365752