Delay-dependent exponential stability of cellular neural networks with time-varying delays

The global exponential stability of cellular neural networks (CNNs) with time-varying delays is analyzed. Two new sufficient conditions ensuring global exponential stability for delayed CNNs are obtained. The conditions presented here are related to the size of delay. The stability results improve the earlier publications. Two examples are given to demonstrate the effectiveness of the obtained results.     

New stability criteria for neural networks with time-varying delays

This paper is concerned with the stability analysis problem of neural networks with time delays. The delay intervals [−d(t), 0] and [−h, 0] are divided into m subintervals with equal length. Some free matrices are introduced to build the relationship among the elements of the resultant matrix inequalities. With the above operations, the new stability criteria are built for the general class of neural networks. The conditions are presented in the form of linear matrix inequalities (LMIs), which can be solved by the numerically efficient Matlab LMI toolbox. Several examples are provided to show that our methods are much less conservative than recently reported ones.     

Delay-dependent global asymptotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters

This paper investigates the delay-dependent global asymptotic stability problem of stochastic genetic regulatory networks (SGRNs) with Markovian jumping parameters. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are globally asymptotically stable in the mean square. Distinct difference from other analytical approaches lies in “linearization” of the genetic regulatory networks (GRNs) model, by which the considered GRN model is transformed into a linear system. Then, a process, which is called parameterized first-order model transformation is used to transform the linear system. Novel criteria for global asymptotic stability of the SGRNs with constant delays are obtained. Some numerical examples are given to illustrate the effectiveness of our theoretical results.     

Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates

In this paper, the problem of stochastic stability criterion of Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates is considered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Novel delay-dependent asymptotic stability criteria for neural networks with time-varying delays

The problem of delay-dependent asymptotic stability criteria for neural networks (NNs) with time-varying delays is investigated. An improved linear matrix inequality based on delay-dependent stability test is introduced to ensure a large upper bound for time-delay. A new class of Lyapunov function is constructed to derive a novel delay-dependent stability criteria. Finally, numerical examples are given to indicate significant improvement over some existing results.     

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.     

Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays

This paper discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. Some novel global stability criteria of the system is derived by using Lyapunov method, linear matrix inequality (LMI) and analytic technique. The LMI-based criteria obtained here are computationally more flexible and more generic than many other existing criteria. A numerical example is given to illustrate our result.     

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.     

Delay-dependent asymptotic stability for neural networks with distributed delays

In this paper, dynamical behavior of a class of neural networks with distributed delays is studied by employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical Hopfield neural networks with distributed delays and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature.     

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.     

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.     

Delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with mixed time-varying delays: An LMI approach

This paper investigates the delay-probability-distribution-dependent stability problem of uncertain stochastic genetic regulatory networks (SGRNs) with mixed time-varying delays. The information of the probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred SGRNs model. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are robustly globally asymptotically stable in the mean square for all admissible uncertainties. Finally a numerical example is given to illustrate the effectiveness of our theoretical results.     

Improved global exponential stability criteria of cellular neural networks with time-varying delays

In this paper, the existence and uniqueness of the equilibrium point and stability of the cellular neural networks (CNNs) with time-varying delays are analyzed and proved. Several global exponential stability conditions of the neural networks are obtained by the delay differential inequality and matrix measures approach. The obtained results are extensions of the earlier literature. The approach used in this paper is also suitable for delayed Hopfield neural networks and delayed bi-directional associative memory neural networks whose activation functions are often nondifferentiable or unbounded. Two simulation examples in comparison to previous results in literature are shown to check the theory in this paper.     

Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay

This paper proposes an approach for the robust stability of uncertain systems with interval time-varying delay. The key features of the approach include the introduction of uncorrelated augmented matrix items into the Lyapunov functional and the use of a tighter bounding technology. Unlike existing methodologies, the proposed approach involves neither free weighting matrices nor any model transformation. It can, however, lead to much less conservative stability criteria than the existing ones for the systems under consideration. Numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort.     

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.     

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 of neutral systems with time-varying delays using delay-decomposition approach

This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov-Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Delay-dependent exponential stability for a class of neural networks with time delays

This paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. In terms of a linear matrix inequality (LMI), a sufficient condition guaranteeing the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed. This condition is dependent on the size of the time delay, which is usually less conservative than delay-independent ones. The proposed LMI condition can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

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.