期刊
NONLINEAR ANALYSIS-HYBRID SYSTEMS
卷 6, 期 4, 页码 988-1001出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.nahs.2012.07.002
关键词
Hybrid nonlinear systems; Dynamical networks; Input-to-state stability; Small-gain; Lyapunov function
资金
- NYU and POLY
- NSF [DMS-0906659]
- Australian Research Councils [FF0455875]
- Australian Research Council [FF0455875] Funding Source: Australian Research Council
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0906659] Funding Source: National Science Foundation
This paper presents a Lyapunov-based cyclic-small-gain theorem for the hybrid dynamical networks composed of input-to-state stable (ISS) subsystems whose motions may be continuous, impulsive or piecewise constant on the time-line. On the one hand, it is shown that hybrid dynamic networks with interconnection gains less than the identity function are ISS by means of Lyapunov functions. Additionally, an ISS-Lyapunov function for the total network is constructed using the ISS-Lyapunov functions of the subsystems. On the other hand, a novel result of this paper shows that a hybrid dynamic network satisfying the cyclic-small-gain condition can be transformed into one with interconnection gains less than the identity. In sharp contrast with several previously known results, the impulses of the subsystems are time triggered and the impulsive times for different subsystems may be different. (C) 2012 Elsevier Ltd. All rights reserved.
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