Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks

Tengfei Liu, Zhong Ping Jiang, David J. Hill

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


This paper develops a cyclic-small-gain theorem for hybrid dynamical networks composed of continuous-time and discrete-time input-to-state stable (ISS) subsystems. The main result is achieved in two steps: a) A hybrid dynamical network composed of ISS subsystems with interconnection gains less than the identity is ISS; b) Any hybrid dynamical networks satisfying the cyclic-small-gain condition can be transformed into networks with interconnection gains less than the identity. The sampling times of the discrete-time subsystems are independent of the states, which makes this result different from several of the existing results.

Original languageEnglish (US)
Title of host publication8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010
PublisherIFAC Secretariat
Number of pages6
ISBN (Print)9783902661807
StatePublished - 2010

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


  • Cyclic-small-gain
  • Hybrid systems
  • Lyapunov formulation

ASJC Scopus subject areas

  • Control and Systems Engineering


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