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.     

On the stability of impulsive functional differential equations with infinite delays

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd.     

Asymptotic synchronization of continuous/discrete complex dynamical networks by optimal partitioning method

The synchronization problem for both continuous and discrete‐time complex dynamical networks with time‐varying delays is investigated. Using optimal partitioning method, time‐varying delays are partitioned into l subintervals and generalized results are derived in terms of linear matrix inequalities (LMIs). New delay‐dependent synchronization criteria in terms of LMIs are derived by constructing appropriate Lyapunov–Krasovskii functional, reciprocally convex combination technique and some inequality techniques. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2014 Wiley Periodicals, Inc. Complexity 21: 193–210, 2015     

Existence,uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations

In this paper, a class of recurrent neural networks with time delay in the leakage term under impulsive perturbations is considered. First, a sufficient condition is given to ensure the global existence and uniqueness of the solution for the addressed neural networks by using the contraction mapping theorem. Then, we present some sufficient conditions to guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point by using topological degree theory, Lyapunov–Kravsovskii functionals and some analysis techniques. The proposed results, which do not require the boundedness, differentiability and monotonicity of the activation functions, can be easily checked via the linear matrix inequality (LMI) control toolbox in MATLAB. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. In the absence of leakage delay, the results obtained are also new results. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This Letter is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI) and by introducing some free-weighting matrices. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time‐varying delays

This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time‐varying delays. The jumping parameters are represented as a continuous‐time discrete‐state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time‐varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay‐dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016     

Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the global asymptotical stability analysis problem is considered for a class of Markovian jumping stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. An alternative delay-dependent stability analysis result is established based on the linear matrix inequality (LMI) technique, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Neither system transformation nor free weight matrix via Newton–Leibniz formula is required. Two numerical examples are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature.