Robust non-fragile H∞H∞ state estimation for discrete-time genetic regulatory networks with Markov jump delays and uncertain transition probabilities

This paper addresses the problem of robust non-fragile H∞H∞ state estimation for discrete-time genetic regulatory networks (GRNs) with exogenous disturbances, parameter uncertainties, and time delays. The network parameters are assumed to be time-varying but norm-bounded to account for the unavoidable modeling errors and parameter fluctuations. Two different Markov chains with uncertain transition probabilities are utilized to model the feedback regulation delay and the translation delay. We aim to estimate the true concentrations of mRNAs and proteins by designing a non-fragile H∞H∞ estimator such that the estimation error dynamics is stochastically stable while achieving the prescribed H∞H∞ disturbance attenuation level. By constructing a mode-dependent Lyapunov–Krasovskii functional, a sufficient condition for the existence of the desired estimator is derived in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the estimator gains can be explicitly given. An illustrative example is given to demonstrate the effectiveness of our results.