Robust μ-stability analysis of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays

This paper investigates the global robust stability problem of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays and norm bounded parameter uncertainties. The structure variations at discrete time instances during the process of gene regulations known as hybrid genetic regulatory networks based on Markov process is proposed. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The concept of global robust μ-stability in the mean square for genetic regulatory networks is given. Based on Lyapunov function, stochastic theory and Itô’s differential formula, the stability criteria are presented in the form of linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the effectiveness of the main result.

► Global robust μ-stability results are derived in terms of linear matrix inequalities.
► Markovian jumping parameters and unbounded time varying delays are considered.
► The results are derived by using Lyapunov–Krasovskii functional, stochastic theory and Itô’s differential formula.
► Numerical examples are presented to illustrate the usefulness of the derived results.