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. (C) 2015 Elsevier B.V. All rights reserved.