Passivity and passification for Markov jump genetic regulatory networks with time-varying delays

Distributed nonsynchronous event-triggered state estimation of genetic regulatory networks with hidden Markovian jumping parameters

In this paper, the distributed state estimation problem of genetic regulatory networks (GRNs) with hidden Markovian jumping parameters (HMJPs) is explored. Furthermore, in order to improve the communication efficiency among state estimation sensors, the event-triggered strategy is employed in the distributed framework for sensor networks. Particularly, by considering the fact that the true modes are always unaccessible, a novel nonsynchronous state estimation (NSE) strategy is utilized based on observed hidden mode information. By means of Lyapunov-Krasovski method, sufficient stochastic state estimation analysis and synthesis results are established, such that the concentrations of mRNA and protein in GRNs can be both well estimated by convex optimization. Finally, an illustrative example with relevant simulations results is provided to validate the applicability and effectiveness of the developed state estimation approach.

Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

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.

Non-fragile mixed H∞ and passive synchronization of Markov jump neural networks with mixed time-varying delays and randomly occurring controller gain fluctuation

This paper studies the non-fragile mixed H∞ and passive synchronization problem for Markov jump neural networks. The randomly occurring controller gain fluctuation phenomenon is investigated for non-fragile strategy. Moreover, the mixed time-varying delays composed of discrete and distributed delays are considered. By employing stochastic stability theory, synchronization criteria are developed for the Markov jump neural networks. On the basis of the derived criteria, the non-fragile synchronization controller is designed. Finally, an illustrative example is presented to demonstrate the validity of the control approach.

Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach

In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.

Globally Asymptotic Stability Analysis for Genetic Regulatory Networks with Mixed Delays: An M-Matrix-Based Approach

This paper deals with the problem of globally asymptotic stability for nonnegative equilibrium points of genetic regulatory networks (GRNs) with mixed delays (i.e., time-varying discrete delays and constant distributed delays). Up to now, all existing stability criteria for equilibrium points of the kind of considered GRNs are in the form of the linear matrix inequalities (LMIs). In this paper, the Brouwer's fixed point theorem is employed to obtain sufficient conditions such that the kind of GRNs under consideration here has at least one nonnegative equilibrium point. Then, by using the nonsingular M-matrix theory and the functional differential equation theory, M-matrix-based sufficient conditions are proposed to guarantee that the kind of GRNs under consideration here has a unique nonnegative equilibrium point which is globally asymptotically stable. The M-matrix-based sufficient conditions derived here are to check whether a constant matrix is a nonsingular M-matrix, which can be easily verified, as there are many equivalent statements on the nonsingular M-matrices. So, in terms of computational complexity, the M-matrix-based stability criteria established in this paper are superior to the LMI-based ones in literature. To illustrate the effectiveness of the approach proposed in this paper, several numerical examples and their simulations are given.