Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback

Details Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback

Publishing date

2001-12-20

URL

arxiv.org/abs/math/0112232v1

Science

Mathematics

Field

Optimization and Control

Additional info

Updates and replaces math.OC/0112021 See http://www.math.rutgers.edu/~sontag/ for related work

Type

Scientific paper

Abstract

The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly feedback-dependent, steady states. A Lyapunov-like characterization allows the computation of gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops. An application in biology (MAPK signaling) is worked out in detail.

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