This paper investigates the H _∞ state estimation problem for a class of discrete-time nonlinear singularly perturbed complex networks (SPCNs) under the Round-Robin (RR) protocol. A discrete-time nonlinear SPCN model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter (SPP). The network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the RR protocol with hope to avoid the undesired data collision. The error dynamics of the state estimation is governed by a switched system with a periodic switching parameter. A novel Lyapunov function is constructed that is dependent on both the transmission order and the SPP. By establishing a key lemma specifically tackling the SPP, sufficient conditions are obtained such that, for any SPP less than or equal to a predefined upper bound, the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed H _∞ performance requirement. Furthermore, the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities, and the upper bound of the SPP is then evaluated in the feasibility of these matrix inequalities. Moreover, the corresponding results for linear discrete-time SPCNs are derived as corollaries. A numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme.

This paper investigates the problem of finite-time H _∞ 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 H _∞ 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.

This paper investigates the problem of state estimation for discrete time-delayed genetic regulatory networks with stochastic process noises and bounded exogenous disturbances under the Round-Robin (RR) protocols. The network measurement outputs obtained by two groups of sensors are transmitted to two remote sub-estimators via two independent communication channels, respectively. To lighten the communication loads of the networks and reduce the occurrence rate of data collisions, two RR protocols are utilized to orchestrate the transmission orders of sensor nodes in two groups, respectively. The error dynamics of the state estimation is governed by a switched system with periodic switching parameters. By constructing a transmission-order-dependent Lyapunov-like functional and utilizing the up-to-date discrete Wirtinger-based inequality together with the reciprocally convex approach, sufficient conditions are established to guarantee the exponentially ultimate boundedness of the estimation error dynamics in mean square with a prescribed upper bound on the decay rate. An asymptotic upper bound of the outputs of the estimation errors in mean square is derived and the estimator parameters are then obtained by minimizing such an upper bound subject to linear matrix inequality constraints. The repressilator model is utilized to illustrate the effectiveness of the designed estimator.

The issue of finite-time H∞ state estimation is studied for a class of discrete-time nonlinear two-time-scale complex networks (TTSCNs) whose measurement outputs are transmitted to a remote estimator via a bandwidth-limited communication network under the stochastic communication protocol (SCP). To reflect different time scales of state evolutions, a new discrete-time TTSCN model is devised by introducing a singular perturbation parameter (SPP). For the sake of avoiding/alleviating the undesirable data collisions, the SCP is adopted to schedule the data transmissions, where the transition probabilities involved are assumed to be partially unknown. By constructing a new Lyapunov function dependent on the information of the SCP and SPP, a sufficient condition is derived which ensures that the resulting error dynamics is stochastically finite-time bounded and satisfies a prescribed H∞ performance index. By resorting to the solutions of several matrix inequalities, the gain matrices of the state estimator are given and the admissible upper bound of the SPP can be evaluated simultaneously. The performance of the designed state estimator is demonstrated by two examples.

This paper deals with the finite-horizon quantized H _∞ state estimation problem for a class of discrete timevarying genetic regulatory networks with quantization effects under stochastic communication protocols (SCPs). To better reflect the data-driven flavor of today's biological research, the network measurements (typically gigabytes in size by highthroughput sequencing technologies) are transmitted to a remote state estimator via two independent communication networks of limited bandwidths. To lighten the communication loads and avoid undesired data collisions, the measurement outputs are quantized and then transmitted under two SCPs introduced to schedule the large-scale data transmissions. The purpose of this paper is to design a time-varying state estimator such that the error dynamics of the state estimation satisfies a prescribed H _∞ performance requirement over a finite horizon in the presence of nonlinearities, quantization effects, and SCPs. By utilizing the completing-the-square technique, sufficient conditions are derived to ensure the H _∞ estimation performance and the parameters of the state estimator are designed by solving coupled backward recursive Riccati difference equations. A numerical example is given to illustrate the effectiveness of the design scheme of the proposed state estimator.