Fixed-Time Synchronization Analysis of Genetic Regulatory Network Model with Time-Delay

The synchronous genetic regulatory networks model includes the drive system and response system, and the drive-response system is symmetric. From a biological point of view, this model illustrates the dynamic behaviors in gene-to-protein processes, in terms of transcription and translation. This paper introduces a model of genetic regulatory networks with time delay. The fixed-time synchronization control problem of the proposed model is studied based on fixed-time stability theory and the Lyapunov method. Concretely, the authors first propose a way to switch from the given model to matrix form. Then, two types of novel controllers are designed and the corresponding sufficient conditions are investigated respectively to ensure the fixed-time synchronization goal. Moreover, the settling times of fixed-time synchronization are estimated for the addressed discontinuous controllers, which are not dependent on the initial or delayed states of the model. Finally, numerical simulations are presented and compared to illustrate the benefits of the theoretical results.

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.

Dissipativity-Based Filtering for Switched Genetic Regulatory Networks with Stochastic Disturbances and Time-Varying Delays

This paper deals with the problem of dissipativity-based filtering for switched genetic regulatory networks (GRNs) with stochastic perturbation and time-varying delays. By choosing an appropriate piecewise Lyapunov function and using the average dwell time method, we propose a new set of sufficient conditions in terms of Linear matrix inequalities (LMIs) for the existence of dissipative filter, which ensures that the resulting filtering error system is mean-square exponentially stable with dissipativity performance. The filter gains are provided by solving feasible solutions to a certain set of LMIs. A simulation example is given to demonstrate the effectiveness of the desired dissipativity-based filter design approach.

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

In this paper, the sufficient conditions for the global exponential stability of the switched genetic regulatory networks with mixed time delays are obtained. The proposed method does not need the construction of Lyapunov-Krasovskii functional, but is directly proceeded by the definition of global exponential stability. The derived sufficient conditions can easily be verified by checking the eigenvalues of a constant matrix or solving several simple linear matrix inequalities. Finally, two numerical examples are presented to illustrate that the obtained global exponential stability criteria are available.

Stability Analysis of Genetic Regulatory Networks With General Random Disturbances

This paper establishes the stability criteria for genetic regulatory networks with random disturbances. We assume the nonlinear feedback regulation function to satisfy the sector-like condition and the random perturbation to have a finite second-order moment. First, under the globally Lipschitz condition, the existence and uniqueness of solution to random genetic regulatory networks are considered by exploiting an iterative approximation method. Then, by feat of the random analysis method and matrix technique, sufficient conditions are given to guarantee the noise-to-state stability in mean and globally asymptotic stability in probability, respectively. At last, two simulation examples are exploited in order to verify the validity of the proposed theory.

Model Approximation for Switched Genetic Regulatory Networks

The model approximation problem is studied in this paper for switched genetic regulatory networks (GRNs) with time-varying delays. We focus on constructing a reduced-order model to approximate the high-order GRNs considered under the switching signal subject to certain constraints, such that the approximation error system between the original and reduced-order systems is exponentially stable with a disturbance attenuation performance. The stability conditions and the disturbance attenuation performance are established by utilizing two integral inequality bounding techniques and the average dwell-time method for the approximation error system. Then, the solvability conditions for the reduced-order models for the GRNs are also established using the projection method. Furthermore, the model approximation problem can be transferred into a sequential minimization problem that is subject to linear matrix inequality constraints by using the cone complementarity algorithm. Finally, several examples are provided to illustrate the effectiveness and the advantages of the proposed methods.

Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.