Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback. Sontag, E. Systems Control Lett., 47(2):167–179, 2002. abstract bibtex 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.
@ARTICLE{cauchySCL02,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Asymptotic amplitudes and Cauchy gains: A small-gain
principle and an application to inhibitory biological feedback},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {167--179},
VOLUME = {47},
KEYWORDS = {cyclic feedback systems, small-gain},
PDF = {../../FTPDIR/cauchy-gains-scl-as-published.pdf},
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. }
}