New Method to Global Exponential Stability Analysis for Switched Genetic Regulatory Networks With Mixed Delays

State estimation for delayed genetic regulatory networks with reaction diffusion terms and Markovian jump

Robust state estimation for delayed genetic regulatory networks with reaction–diffusion terms and uncertainties terms under Dirichlet boundary conditions is addressed in this article. The main purpose of the problem investigation is to design a novel state observer for estimate the true concentrations of mRNA and protein by available measurement outputs. Based on Lyapunov–Krasovskii functions and linear matrix inequalities (LMI), sufficient conditions are given to ensure the robust stability of the estimation error networks. Two examples are presented to illustrate the effectiveness of the proposed approach.

Finite-Time H∞ State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties

This article is concerned with the problem of finite-time H_∞ state estimation for switched genetic regulatory networks with randomly occurring uncertainties. The persistent dwell-time switching rule, as a more versatile class of switching rules, is considered in this paper. Besides, several random variables that obey the Bernoulli distribution are used to represent randomly occurring uncertainties. The overriding purpose of this article is to design an estimator to ensure that the estimation error system is stochastically finite-time bounded and satisfies the H_∞ performance. Based on this, sufficient conditions for the explicit form of the estimator gains can be obtained by the Lyapunov method. Finally, a numerical example is given to verify the correctness and feasibility of the proposed method.

Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays

This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of an almost periodic state of the model are investigated and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. In addition, sufficient conditions for the global Mittag–Leffler stability of the almost periodic solutions are proposed. To justify our findings a numerical example is also presented.

Space-Dividing-Based Cluster Synchronization of Reaction-Diffusion Genetic Regulatory Networks via Intermittent Control

In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.