@inproceedings{7578c5c6d8354cba88b370c72fece19c,

title = "Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks",

abstract = "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.",

keywords = "Cyclic-small-gain, Hybrid systems, Lyapunov formulation",

author = "Tengfei Liu and Jiang, {Zhong Ping} and Hill, {David J.}",

note = "Funding Information: ★ This research was supported under the Australian Research Councils Discovery funding scheme (project number: FF0455875), in part by a seed grant from NYU and POLY, and by NSF grant DMS-0906659.",

year = "2010",

doi = "10.3182/20100901-3-IT-2016.00016",

language = "English (US)",

isbn = "9783902661807",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "IFAC Secretariat",

number = "14",

pages = "813--818",

booktitle = "8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010",

edition = "14",

}