Title data
Katz, Rami ; Kriecherbauer, Thomas ; Grüne, Lars ; Margaliot, Michael:
On the gain of entrainment in a class of weakly contractive bilinear control systems.
In: SIAM Journal on Control and Optimization.
Vol. 62
(2024)
Issue 5
.
 pp. 27232749.
ISSN 10957138
DOI: https://doi.org/10.1137/23M1585714
This is the latest version of this item.
Related URLs
Project information
Project title: 
Project's official title Project's id Analysis of Random Transport in Chains using Modern Tools from Systems and Control Theory GR 1569/241, KR 1673/71, project no.470999742 

Project financing: 
Deutsche Forschungsgemeinschaft Israel Science Foundation Grant 407/19 
Abstract in another language
We consider a class of bilinear weakly contractive systems that entrain to periodic excitations. Entrainment is important in many natural and artificial processes. For example, in order to function properly synchronous generators must entrain to the frequency of the electrical grid, and biological organisms must entrain to the 24h solar day. A dynamical system has a positive gain of entrainment (GOE) if entrainment also yields a larger output, on average. This property is important in many applications from the periodic operation of bioreactors to the periodic production of proteins during the cell cycle division process. We derive a closedform formula for the GOE to firstorder in the control perturbation. This is used to show that in the class of systems that we consider the GOE is always a higherorder phenomenon. We demonstrate the theoretical results using two applications: the master equation and a model from systems biology called the ribosome flow model, both with timevarying and periodic transition rates.
Further data
Available Versions of this Item

On the gain of entrainment in a class of weakly contractive bilinear control systems with applications to the master equation and the ribosome flow model. (deposited 11 Jul 2023 06:21)
 On the gain of entrainment in a class of weakly contractive bilinear control systems. (deposited 04 Oct 2024 08:29) [Currently Displayed]