Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions

Hiroshi Ito, Zhong Ping Jiang, Sergey N. Dashkovskiy, Björn S. R̈uffer

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1192-1207
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - May 2013


  • Integral input-to-state stability (iISS)
  • Large-scale systems
  • Lyapunov functions
  • Nonlinear systems
  • Robust stability criteria

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


Dive into the research topics of 'Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions'. Together they form a unique fingerprint.

Cite this