Revising regulatory networks: from expression data to linear causal models
Journal of Biomedical Informatics
Brief Homogeneous Lyapunov functions for systems with structured uncertainties
Automatica (Journal of IFAC)
International Journal of Systems Science - Dynamics Analysis of Gene Regulatory Networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
Robust stability for uncertain genetic regulatory networks with interval time-varying delays
Information Sciences: an International Journal
Mean square exponential stability of stochastic genetic regulatory networks with time-varying delays
Information Sciences: an International Journal
Robustness analysis of genetic regulatory networks affected by model uncertainty
Automatica (Journal of IFAC)
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This paper addresses the problem of establishing robust stability of uncertain genetic networks with sum regulatory functions. Specifically, we first consider uncertain genetic networks where the regulation occurs at the transcriptional level, and we derive a sufficient condition for robust stability by introducing a bounding set of the uncertain nonlinearity. We hence show that this condition can be formulated as a convex optimization through polynomial Lyapunov functions and polynomial descriptions of the bounding set by exploiting the square matricial representation (SMR) of polynomials which allows to establish whether a polynomial is a sum of squares (SOS) via a linear matrix inequality (LMI). Then, we propose a method for computing a family of bounding sets by means of convex optimizations. It is worthwhile to remark that these results are derived in spite of the fact that the variable equilibrium point cannot be computed as being the solution of a system of parameter-dependent nonlinear equations, and is hence unknown. Lastly, the proposed approach is extended to models where the regulation occurs at different levels and both mRNA and protein dynamics are nonlinear.