Robust filtering of uncertain stochastic genetic regulatory networks with time-varying delays

This study is concerned with the problem of robust filtering for stochastic genetic regulatory networks with time-varying delays and parameter uncertainties. By choosing an appropriate novel Lyapunov–Krasovskii functional and establishing a new integral inequality in the stochastic setting, less conservative conditions are obtained to ensure the error systems are mean-square robustly asymptotically stable. Then the filters are designed in terms of linear matrix inequalities (LMIs) which can be checked efficiently via the LMI toolbox. What is more, the criteria can be applicable to both fast and slow time-varying delays due to our careful consideration of the ranges for the time-varying delays. Finally, two examples are presented to illustrate the effectiveness and advantages of the theoretical results.     

Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: An LMI approach

In this paper, we consider the stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. By utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, some sufficient LMI-based conditions are obtained to guarantee the global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. These conditions can be easily checked via the MATLAB LMI toolbox. Moreover, the obtained results extend and improve the earlier publications. Finally, a numerical example is provided to demonstrate the low conservatism and effectiveness of the proposed LMI conditions.     

An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays

This paper deals with the problem of global exponential stability for a general class of stochastic high-order neural networks with mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both mixed time delays and Markovian switching. By employing a new Lyapunov–Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, and hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.     

Robust asymptotic stability for BAM neural networks with time-varying delays via LMI approach

Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.     

Passivity analysis for stochastic Markovian switching genetic regulatory networks with time-varying delays

In this paper, the passivity problem for the stochastic Markovian switching genetic regulatory networks with time-varying delays is investigated. By applying control theory and mathematical tools, a sufficient condition for this problem is obtained and presented in terms of linear matrix inequalities (LMIs), which can be easily verified by Matlab LMI toolbox. The obtained condition provides some insight into synthetic biology and systems biology. Finally, a numerical example is given to show the effectiveness of the proposed result.     

Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays

The problem of stochastic robust stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are time-varying and norm-bounded. The time-delay factors are unknown and time-varying with known bounds. Based on Lyapunov–Krasovskii functional and stochastic analysis approaches, some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.     

Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach

In this paper, the robust asymptotic stability problem is considered for a class of fuzzy Markovian jumping genetic regulatory networks with uncertain parameters and switching probabilities by delay decomposition approach. The purpose of the addressed stability analysis problem is to establish an easy-to-verify condition under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov–Krasovskii functional (LKF) is constructed by nonuniformly dividing the delay interval into multiple subinterval, and choosing proper functionals with different weighting matrices corresponding to different subintervals in the LKFs. Employing these new LKFs for the time-varying delays, a new delay-dependent stability criterion is established with Markovian jumping parameters by T–S fuzzy model. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are exploited to illustrate the effectiveness of the proposed design procedures.     

Delay-dependent stability criteria for genetic regulatory networks with time-varying delays and nonlinear disturbance

This paper presents the robust stability of genetic regulatory networks with time-varying delays and nonlinear disturbance. By choosing an appropriate new Lyapunov functional, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs). The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.     

Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays

In this paper, the stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks (GRNs) with mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov-Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotically stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results.     

LMI approach to exponential stability of linear systems with interval time-varying delays

This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov–Krasovskii functional combined with the Newton–Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results.     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criteria.     

Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays

This paper deals with the synchronization problem for competitive neural networks with different time scales, as well as mixed time-varying delays (both discrete and distributed time-varying delays) and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, an adaptive feedback controller is proposed to guarantee the exponential synchronization of proposed competitive neural networks in terms of p-norm. The synchronization results presented in this paper generalize and improve many known results. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the theoretical results.     

Exponential stability of hybrid stochastic recurrent neural networks with time-varying delays

In this paper, we consider a class of hybrid Stochastic recurrent neural networks with time-varying delays. By using Razumikhin-type theorem, we not only obtain–almost surely–the exponential stability but also estimate the exponentially convergent rate.     

Exponential stability analysis of uncertain stochastic neural networks with multiple delays

This paper addresses the stability analysis problem for stochastic neural networks with parameter uncertainties and multiple time delays. The delays are time varying, and the parameter uncertainties are assumed to be norm bounded. A sufficient condition is derived such that for all admissible uncertainties, the considered neural network is globally exponentially stable in the mean square. The stability criterion is formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily checked in practice. Finally, a numerical example is provided to illustrate the proposed result.     

New robust stability criteria for uncertain neural networks with interval time-varying delays

In this paper, problem of robust stability of uncertain neural networks with interval time-varying delays has been investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional approach, a new delay-dependent stability criteria is presented in terms of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays

In this paper, the global asymptotic stability is investigated for a class of neutral stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stability theory and stochastic analysis approaches, delay-dependent criteria are derived to ensure the global, robust, asymptotic stability of the addressed system in the mean square for all admissible parameter uncertainties. The criteria can be checked easily by the LMI Control Toolbox in Matlab. A numerical example is given to illustrate the feasibility and effectiveness of the results.     

Mean square exponential stability in high-order stochastic impulsive neural networks with time-varying delays

In this paper, we consider a class of stochastic impulsive high-order neural networks with time-varying delays. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order neural networks.     

Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic bidirectional associative memory (BAM) neural networks with reaction-diffusion and mixed delays. The mixed delays considered in this paper are time-varying and distributed delays. Based on a new Lyapunov-Krasovskii functional and the Poincaré inequality as well as stochastic analysis theory, a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Moreover, two numerical examples are given to show the effectiveness of the theoretical results.     

Exponential stability for stochastic jumping BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic jumping bidirectional associative memory (BAM) neural networks with time-varying and distributed delays. To the best of our knowledge, this class of stochastic jumping BAM neural networks with time-varying and distributed delays has never been investigated in the literature. The main aim of this paper tries to fill the gap. By using the stochastic stability theory, the properties of a Brownian motion, the generalized Ito’s formula and linear matrix inequalities technique, some novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. In particular, the activation functions considered in this paper are fairly general since they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, the derivative of time delays is not necessarily zero or small than 1. In summary, the results obtained in this paper extend and improve those not only with/without noise disturbances, but also with/without Markovian jump parameters. Finally, two interesting examples are provided to illustrate the theoretical results.