Robust stability of uncertain genetic regulatory networks with multivariable regulation functions

This paper investigates robust stability of uncertain genetic regulatory networks (GRNs). It is assumed that the uncertainties are in the form of a parameter vector that determines the coefficients of the model via given functions. And the novel multivariable regulation functions are introduced here to describe the underlying relationship between different biochemical substance. Firstly, it is shown that, by using Lyapunov functional method and linear matrix inequality technology (LMI), a criteria is established to ensure the robust asymptotical stability of GRNs. Moreover, it is also shown that by using the square matrix representation (SMR) of matrix polynomials and by adopting polynomially parameter-dependent Lyapunov functions, a condition in form of linear matrix inequalities (LMIs) for robust stability for all admissible uncertainties can be obtained. An example with real biological model is provided to illustrate the use of the proposed methodology.