Finite-Time $H_{\infty}$ State Estimation for Discrete Time-Delayed Genetic Regulatory Networks Under Stochastic Communication Protocols

This paper investigates the problem of finite-time <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> state estimation for discrete time-delayed genetic regulatory networks under stochastic communication protocols (SCPs). The network measurements are transmitted from two groups of sensors to a remote state estimator via two independent communication channels of limited bandwidths, and two SCPs are utilized to orchestrate the transmission orders of sensor nodes with aim to avoid data collisions. The estimation error dynamics is modeled by a Markovian switching system with two switching signals. By constructing a transmission-order-dependent Lyapunov–Krasovskii functional and utilizing an up-to-date discrete Wirtinger-based inequality together with the reciprocally convex approach, sufficient conditions are established to guarantee the stochastic finite-time boundedness for the estimation error dynamics with a prescribed <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> disturbance attenuation level. The parameters of the state estimator are designed by solving a convex optimization problem which minimizes the disturbance attenuation level subject to several inequality constraints. The repressilator model is utilized to illustrate the effectiveness of the design procedure of the proposed state estimator.