On the Stability of Piecewise Genetic Regulatory Networks

Abstract

The hybrid dynamics of the genetic regulatory networks (GRNs) have attracted much research attention in recent years. This paper is concerned with the stability analysis of piecewise GRNs. Depending on whether the state partitions and mode transitions are known or unknown as a priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, by using common polynomial Lyapunov functions and piecewise polynomial Lyapunov functions, two conditions are established to ensure the globally asymptotically stability for switched and hybrid GRNs, respectively. Moreover, it is shown that, by using the sum of squares (SOS) techniques, stability conditions in form of linear matrix inequalities (LMIs) for both models can be obtained. An example with synthetic hybrid GRN model is provided to illustrate the use of the proposed methodology.