Mode-mismatched estimator design for Markov jump genetic regulatory networks with random time delays

In this paper, the problem of H_∞ state estimation is investigated for a class of discrete-time Markov jump genetic regulatory networks (GRNs) with random time delays. A mismatching characteristic of modes jumping between GRNs modes and desired mode-dependent estimators is recognized, and a nonstationary mode transition among the estimators is used to model the mismatching characteristic of modes jumping to different degrees. The time delays are supposed to be time-varying and subject to another Markov chain. By using the linear matrix inequality techniques, sufficient conditions on the existence of the estimators with mismatching characteristic of modes jumping are first derived such that the resulting estimation error system is stochastically stable with a prescribed H_∞ performance index. One interesting phenomenon is disclosed, i.e., the optimal performance index varies monotonously as changing the mismatching degrees of modes jumping. A numerical example is exploited to illustrate the effectiveness of the theoretical findings.