Imperial College London
Portrait Picture

Prof David Angeli

Faculty of Engineering, Department of Electrical and Electronic Engineering

Professor of Nonlinear Network Dynamics
 
 
 
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Contact

 

+44 (0)20 7594 6283d.angeli Website

 
 
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Location

 

1107CElectrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Pasquini:2021:10.1007/s00285-021-01690-3,
author = {Pasquini, M and Angeli, D},
doi = {10.1007/s00285-021-01690-3},
journal = {Journal of Mathematical Biology},
pages = {1--38},
title = {On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach},
url = {http://dx.doi.org/10.1007/s00285-021-01690-3},
volume = {83},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.
AU  - Pasquini,M
AU  - Angeli,D
DO  - 10.1007/s00285-021-01690-3
EP  - 38
PY  - 2021///
SN  - 0303-6812
SP  - 1
TI  - On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach
T2  - Journal of Mathematical Biology
UR  - http://dx.doi.org/10.1007/s00285-021-01690-3
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000720434100001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00285-021-01690-3
UR  - http://hdl.handle.net/10044/1/93842
VL  - 83
ER  -
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