A global stability criterion for simple control loops, J. Math. Biology, vol.4, pp.363-373, 1977. ,
Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions. ESAIM: Control, Optimisation and Calculus of Variations, vol.4, pp.361-376, 1999. ,
Transient behavior of biological loop models with application to the Droop model, Mathematical Biosciences, vol.127, pp.19-43, 1995. ,
p53 at a glance, J Cell Sci, vol.123, issue.15, pp.2527-2532, 2010. ,
Piecewise-linear models of genetic regulatory networks: equilibria and their stability, Journal of mathematical biology, vol.52, issue.1, pp.27-56, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00071250
A new qualitative control strategy for the genetic toggle switch. IFAC-PapersOnLine, vol.52, pp.532-537, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02319873
Exact control of genetic networks in a qualitative framework: The bistable switch example, Automatica, vol.47, pp.1105-1112, 2011. ,
URL : https://hal.archives-ouvertes.fr/inria-00507040
Modeling and simulation of genetic regulatory systems: a literature review, Journal of computational biology, vol.9, issue.1, pp.67-103, 2002. ,
URL : https://hal.archives-ouvertes.fr/inria-00072606
Control design for sustained oscillation in a two-gene regulatory network, Journal of mathematical biology, vol.62, issue.4, pp.453-478, 2011. ,
A synthetic oscillatory network of transcriptional regulators, Nature, vol.403, pp.335-338, 2000. ,
Periodic solutions of piecewise affine gene network models with non uniform decay rates: the case of a negative feedback loop, Acta Biotheoretica, vol.57, pp.429-455, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00831799
Qualitative control of periodic solutions in piecewise affine models of genetic networks, IFAC Proceedings Volumes, vol.43, pp.326-331, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00831789
, Differential Equations With Discontinuous Righthand Sides. Kluwer, 1988.
In-vivo real-time control of gene expression: a comparative analysis of feedback control strategies in yeast, ACS synthetic biology, vol.5, issue.2, pp.154-162, 2015. ,
Automatic control of gene expression in mammalian cells, ACS synthetic biology, vol.5, issue.4, pp.296-302, 2015. ,
Pathological effect of homeostatic synaptic scaling on network dynamics in diseases of the cortex, Journal of Neuroscience, vol.28, issue.7, pp.1709-1720, 2008. ,
The loss of circadian PAR bZip transcription factors results in epilepsy, Genes & development, vol.18, issue.12, pp.1397-1412, 2004. ,
Oscillations and variability in the p53 system, Molecular systems biology, vol.2, issue.1, 2006. ,
Prediction of limit cycles in mathematical models of biological oscillations, Bulletin of Mathematical Biology, vol.40, pp.27-44, 1978. ,
Temporal organization in cells. A dynamic theory of cellular control processes, 1963. ,
Positive control for global stabilization of predator-prey systems, IFAC Proceedings Volumes, vol.46, pp.265-270, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00850374
Stability of neuronal networks with homeostatic regulation, PLoS computational biology, vol.11, issue.7, p.1004357, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01098491
Existence of periodic solutions for negative feedback cellular control systems, Journal of Differential Equations, vol.25, pp.39-64, 1977. ,
Putting p53 in context, Cell, vol.170, issue.6, pp.1062-1078, 2017. ,
Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study, Proc Natl Acad Sci, vol.97, pp.11250-11255, 2000. ,
Balancing a genetic toggle switch by real-time feedback control and periodic forcing, Nature Communications, vol.8, p.1671, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01666980
Handbook of hybrid systems control: theory, tools, applications, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00450093
Hybrid control of a bioreactor with quantized measurements, IEEE Transactions on automatic control, vol.61, issue.5, pp.1385-1390, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01239387
The Poincare-Bendixson theorem for monotone cyclic feedback systems, Journal of Dynamics and Differential Equations, vol.2, pp.367-421, 1990. ,
Cellular oscillatory mechanisms, vol.641, 2008. ,
Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks, J. Math Biology, vol.5, pp.99-114, 1978. ,
Invivo real-time control of protein expression from endogenous and synthetic gene networks, PLoS computational biology, vol.10, issue.5, 2014. ,
Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth, Nature communications, vol.7, p.12546, 2016. ,
Network motifs: Simple building blocks of complex networks, Science, vol.298, pp.824-827, 2002. ,
Oscillation patterns in negative feedback loops, Proceedings of the National Academy of Sciences, vol.104, issue.16, pp.6533-6537, 2007. ,
Stability notions and Lyapunov functions for sliding mode control systems, Journal of the Franklin Institute, vol.351, issue.4, pp.1831-1865, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00942319
Global asymptotic stability of the Goodwin system with repression, Nonlinear Analysis: Real World Applications, vol.10, pp.2151-2156, 2009. ,
Molecular systems biology and control, European journal of control, vol.11, issue.4-5, pp.396-435, 2005. ,
P53 dysfunction in neurodegenerative diseases-the cause or effect of pathological changes?, Aging and disease, vol.8, issue.4, p.506, 2017. ,
Biological feedback, 1990. ,
URL : https://hal.archives-ouvertes.fr/hal-00087681
Light-based feedback for controlling intracellular signaling dynamics, Nature methods, vol.8, issue.10, pp.837-839, 2011. ,
On the existence of oscillatory solutions in negative feedback cellular control processes, Journal of Mathematical Biology, vol.1, issue.4, pp.311-315, 1975. ,
Long-term model predictive control of gene expression at the population and single-cell levels, Proceedings of the National Academy of Sciences, vol.109, issue.35, pp.14271-14276, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01528440
Conditions for global stability of monotone tridiagonal systems with negative feedback, Systems and Control Letters, vol.59, pp.130-138, 2010. ,