Finite-time stochastic synchronization of genetic regulatory networks

This paper is concerned with the finite-time synchronization for a class of stochastic genetic regulatory networks (GRNs). The purpose of the addressed problem is to design a controller that can synchronize the concentration of the mRNA and the protein of GRNs in finite time with probability. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are first established for ensuring the finite-time stochastic stability of synchronization error in probability. Then, the gain parameters of the controller are obtained by solving a linear matrix inequality and the robust finite-time synchronization is guaranteed for GRNs with uncertain parameters. Compared with the previous references, a continuous finite-time controller is designed to achieve the synchronization objective and a constructive method that may accelerate the convergence is discussed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.