Robustness and Delay Margin Analysis of a Gene Regulatory Network Model

In the past, a special type of nonlinear delay differential system structure was proposed for gene regulatory networks. For this cyclic dynamical system, stability analysis was done using various tools from systems theory. This paper investigates robust stability of an extended gene regulatory network model with time delayed negative feedback. Specifically, the delay margin analysis is done for this system under multiplicative uncertainty. The effect of uncertainty on the delay margin is determined. It is also shown that for particular higher order extensions of the model it is possible to improve the delay margin.