A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks

Hiroshi Ito, Zhong Ping Jiang, Sergey N. Dashkovskiy, Bjorn S. Ruffer

Research output: Contribution to journalConference articlepeer-review


This paper considers nonlinear dynamical networks consisting of individually iISS (integral input-to-state stable) subsystems which are not necessarily ISS (input-to-state stable). Stability criteria for internal and external stability of the networks are developed in view of both necessity and sufficiency. For the sufficiency, we show how we can construct a Lyapunov function of the network explicitly under the assumption that a cyclic small-gain condition is satisfied. The cyclic small-gain condition is shown to be equivalent to a matrix-like condition. The two conditions and their equivalence precisely generalize some central ISS results in the literature. Moreover, the necessity of the matrix-like condition is established. The allowable number of non-ISS subsystems for stability of the network is discussed through several necessity conditions.

Original languageEnglish (US)
Article number6426994
Pages (from-to)4158-4164
Number of pages7
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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