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: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages4158-4164
Number of pages7
DOIs
StatePublished - 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

Other

Other51st IEEE Conference on Decision and Control, CDC 2012
CountryUnited States
CityMaui, HI
Period12/10/1212/13/12

Fingerprint

Stability criteria
Lyapunov functions
Sufficiency
Subsystem
Stability Criteria
Lyapunov Function
Equivalence
Internal
Generalise
Necessity

ASJC Scopus subject areas

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

Cite this

Ito, H., Jiang, Z-P., Dashkovskiy, S. N., & Ruffer, B. S. (2012). A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. In Proceedings of the IEEE Conference on Decision and Control (pp. 4158-4164). [6426994] https://doi.org/10.1109/CDC.2012.6426994

A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. / Ito, Hiroshi; Jiang, Zhong-Ping; Dashkovskiy, Sergey N.; Ruffer, Bjorn S.

Proceedings of the IEEE Conference on Decision and Control. 2012. p. 4158-4164 6426994.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ito, H, Jiang, Z-P, Dashkovskiy, SN & Ruffer, BS 2012, A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. in Proceedings of the IEEE Conference on Decision and Control., 6426994, pp. 4158-4164, 51st IEEE Conference on Decision and Control, CDC 2012, Maui, HI, United States, 12/10/12. https://doi.org/10.1109/CDC.2012.6426994
Ito H, Jiang Z-P, Dashkovskiy SN, Ruffer BS. A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. In Proceedings of the IEEE Conference on Decision and Control. 2012. p. 4158-4164. 6426994 https://doi.org/10.1109/CDC.2012.6426994
Ito, Hiroshi ; Jiang, Zhong-Ping ; Dashkovskiy, Sergey N. ; Ruffer, Bjorn S. / A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks. Proceedings of the IEEE Conference on Decision and Control. 2012. pp. 4158-4164
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