A delay decomposition approach to fuzzy Markovian jumping genetic regulatory networks with time-varying delays

In this paper, we investigated the asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach. The genetic regulatory networks are composed of s modes and the network switches from one mode to another according to a Markovian chain with known transition probabilities. Purpose of this work is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing the whole delay intervals into multiple segments. Choosing proper functionals with different weighting matrices corresponding to different segments in the LKFs. Employing these new LKFs for the case of constant time delays and time-varying delays, some new delay-dependent stability criteria are established with Markovian jumping parameters by T-S fuzzy model. Maximum admissible upper bounds (MAUBs) for the time-varying delays are determined. All the conditions presented here are in the form of linear matrix inequalities (LMI) which are efficiently solved by the LMI toolbox in Matlab. Numerical examples are given to show the effectiveness of the proposed method. (C) 2010 Elsevier B.V. All rights reserved.