Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays

This paper investigates the robust stability problem of a class of discrete-time genetic regulatory networks (GRNs) with probabilistic time delays. Different from the previous works, at each instant the feedback regulation delay and the translation delay are assumed to take values in two given finite sets with deterministic probability distributions. By utilizing a class of indicator functions and discrete-time Jensen inequality, delay-probability-distribution-dependent sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) such that the discrete-time GRNs are robustly asymptotically stable in the mean-square sense for all admissible uncertainties and random delays. Three numerical examples are given to demonstrate the effectiveness of our theoretical results.