2004-29: A Note on a Monotone Small Gain Theorem, with Applications to Delay Systems

DIMACS TR: 2004-29

A Note on a Monotone Small Gain Theorem, with Applications to Delay Systems

Authors: German A. Enciso and Eduardo D. Sontag

ABSTRACT We consider the problem of showing the stability of a dynamical system by writing it as the negative feedback closed loop of a controlled monotone system. We associate to this continuous system a discrete one in a lower dimensional state space, whose global attractivity to an equilibrium implies that of the continuous system to some state. The proofs are given in an abstract setting, and an application is given to a lac operon model with time delay.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-29.ps.gz

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