Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small gain theorems for large scale systems and construction of ISS
  Lyapunov functions   We consider interconnections of n nonlinear subsystems in the input-to-state
stability (ISS) framework. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. A gain matrix is used
to encode the mutual dependencies of the systems in the network. Under a small
gain assumption on the monotone operator induced by the gain matrix, a locally
Lipschitz continuous ISS Lyapunov function is obtained constructively for the
entire network by appropriately scaling the individual Lyapunov functions for
the subsystems. The results are obtained in a general formulation of ISS, the
cases of summation, maximization and separation with respect to external gains
are obtained as corollaries.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int