State estimation for genetic regulatory networks with mode-dependent leakage delays, time-varying delays, and markovian jumping parameters

This paper considers the state estimation problem for Markovian jumping genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays. In order to approximate the true concentrations of the mRNA and protein, the state estimator is designed using available measurement outputs. The GRNs are composed of $N$ modes. The system switches from one mode to another according to a Markovian chain with known transition probabilities. Based on the Lyapunov functionals, including triple integral terms, some inequalities, and a time-varying delay partitioning approach, delay-dependent criteria which employ all upper bounds of time delays of each mode are obtained in terms of linear matrix inequalities (LMIs). This guarantees that the estimation error dynamics can be globally asymptotically stable from solutions of LMIs. Finally, a numerical example is presented to demonstrate the efficiency of the proposed estimation scheme.