An ISS Small-Gain Theorem for General Networks
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In this article, a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems is presented.Abstract:
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.read more
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On characterizations of the input-to-state stability property
Eduardo D. Sontag,Yuan Wang +1 more
TL;DR: In this paper, the Lyapunov sufficient condition for "input-to-state stability" (ISS) is also shown to be necessary and sufficient, which is an open question raised by several authors.
Journal ArticleDOI
Small-gain theorem for ISS systems and applications
TL;DR: This work addresses the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.
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