Asymptotic amplitudes, Cauchy gains, an associated small-gain principle, and an application to inhibitory biological feedback

Author

Sontag, Eduardo D.

Author_Institution

Dept. of Math., Rutgers Univ., New Brunswick, NJ, USA

Volume

4

fYear

2002

fDate

10-13 Dec. 2002

Firstpage

4318

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.

Keywords

Lyapunov methods; asymptotic stability; biocontrol; cascade control; cascade systems; feedback; input-output stability; state-space methods; Cauchy gains; MAPK signaling; asymptotic amplitudes; cascade variety; chaotic behaviors; computation gain; feedback loops; inhibitory biological feedback; input/output systems; small gain principle; state-space systems; steady space systems; steady states; sufficient condition formulation; Biology computing; Chaos; Extraterrestrial measurements; Feedback loop; Mathematics; Output feedback; State estimation; Steady-state; Sufficient conditions; Systems biology;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2002, Proceedings of the 41st IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7516-5

Type

conf

DOI

10.1109/CDC.2002.1185050

Filename

1185050