An ISS Small-Gain Theorem for General Networks

Details An ISS Small-Gain Theorem for General Networks An ISS Small-Gain Theorem for General Networks

2005-06-21

arxiv.org/abs/math/0506434v1

Math. Control Signals Syst. (2007) 19:93-122

Mathematics

Optimization and Control

26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS)

Scientific paper

10.1007/s00498-007-0014-8

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.

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