期刊
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
卷 28, 期 3, 页码 309-344出版社
OXFORD UNIV PRESS
DOI: 10.1093/imamci/dnr001
关键词
input-to-output stability; feedback systems; small-gain theorem; vector Lyapunov functions and functionals
资金
- National Science Foundation [DMS-0504462, DMS-0906659]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0906659] Funding Source: National Science Foundation
A new small-gain theorem is presented for general non-linear control systems and can be viewed as unification of previously developed non-linear small-gain theorems for systems described by ordinary differential equations, retarded functional differential equations and hybrid models. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state stability results. It is shown that the proposed approach is extendible to several important classes of control systems such as large-scale complex systems, non-linear sampled-data systems and non-linear time-delay systems. An application to a biochemical circuit model illustrates the generality and power of the proposed vector small-gain theorem.
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