Unbounded Distributed Delays Research Articles

Finite-Time Stability Analysis of Switched Genetic Regulatory Networks

This paper investigates the finite-time stability problem of switching genetic regulatory networks (GRNs) with interval time-varying delays and unbounded continuous distributed delays. Based on the piecewise Lyapunov-Krasovskii functional and the average dwell time method, some new finite-time stability criteria are obtained in the form of linear matrix inequalities (LMIs), which are easy to be confirmed by the Matlab toolbox. The finite-time stability is taken into account in switching genetic regulatory networks for the first time and the average dwell time of the switching signal is obtained. Two numerical examples are presented to illustrate the effectiveness of our results.

Novel passivity criteria for neural networks with discrete and unbounded distributed time-varying delays

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria.

A New Delay-Dependent Stability Condition for Stochastic Neural Networks of Neutral-Type with Multiple Discrete and Unbounded Distributed Delays

This paper deals with the delay-dependent asymptotic stability analysis problem for stochastic neural networks of neutral- type with mixed delays. The mixed delays comprise both multiple discrete and unbounded distributed delays. To the best of the authors' knowledge, till now, the asymptotic stability problem for this class of neural networks has not yet been solved since neutral-type delays are considered in this paper. The main objective of this paper is to fill this gap. By using Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) technique, a novel sufficient condition is derived to guarantee the global asymptotic stability of the equilibrium point in the mean square. In particular, the proposed stability condition is presented in terms of LMI, which can be easily solved by some standard numerical packages. In addition, an example is given to show the effectiveness of the obtained result.

Robust passive filtering for neutral-type neural networks with time-varying discrete and unbounded distributed delays

The passive filtering problem is studied for a class of neutral-type neural networks with time-varying discrete and unbounded distributed delays. Based on the passive theory, a sufficient condition for the existence of the robust passive filter is given. By introducing an appropriate Lyapunov–Krasovskii functional and using Jensen's inequality technique to deal with its derivative, the criterion which ensures error dynamic system to be strictly passive with dissipation γ>0 is presented in the form of nonlinear matrix inequality. In order to solve the nonlinear problem, a cone complementarity linearization (CCL) algorithm is proposed. Furthermore, when the norm-bounded parameter uncertainties appear in the class of neural networks, the corresponding robust passive filtering problem is also investigated. Three examples are given to demonstrate the effectiveness of the proposed method.

Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Globalμ-Stability Analysis for Impulsive Stochastic Neural Networks with Unbounded Mixed Delays

We investigate the globalμ-stability in the mean square of impulsive stochastic neural networks with unbounded time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, a novel robust stability condition, in the form of linear matrix inequalities, is derived. These sufficient conditions can be tested by MATLAB LMI software packages. The results extend and improve the earlier publication. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

Stability results for impulsive functional differential equations with infinite delay

For a family of differential equations with infinitive delay and impulses, we establish conditions for the existence of global solutions and for the global asymptotic and global exponential stabilities of an equilibrium point. The results are used to give stability criteria for a very broad family of impulsive neural network models with both unbounded distributed delays and bounded time-varying discrete delays. Most of the impulsive neural network models with delay recently studied are included in the general framework presented here.

Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time‐varying delays

SUMMARYThis paper investigates the global asymptotic synchronization in an array of coupled neural networks with random coupling strengths, probabilistic interval time‐varying coupling delays as well as unbounded distributed delays (mixed delays). Two important integral inequalities that include the Jensen's inequality as a special case are developed. On the basis of the developed inequalities, the properties of random variables and Lyapunov functional method, several delay‐dependent sufficient synchronization criteria are derived for the considered model. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using MATLAB LMI Toolbox. Some existing results are improved and extended by taking different values of parameters of the obtained results. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Robust fault detection filter design for a class of neutral‐type neural networks with time‐varying discrete and unbounded distributed delays

SUMMARYThis paper is concerned with the problem of robust fault detection filter design for a class of neutral‐type neural networks with time‐varying discrete and unbounded distributed delays. A Luenberger‐type observer is designed for monitoring fault. By introducing an appropriate Lyapunov–Krasovskii functional and by using Jensen's inequality techniques to deal with its derivative, a new sufficient condition for the existence of robust fault detection filter is proposed in the form of LMIs with nonlinear constraints. To solve the nonlinear problem, a cone complementarity linearization algorithm is proposed. In addition, several numerical examples are provided to illustrate the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs). Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov—Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.

New stability criteria for neutral-type Cohen–Grossberg neural networks with discrete and distributed delays

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results.

New less‐conservative stability results for uncertain stochastic neural networks with fewer slack variables

SUMMARYThe exponential stability problem is investigated for a class of uncertain stochastic neural networks with discrete and unbounded distributed time delays. Two types of uncertainty are considered: one is time‐varying structured uncertainty, whereas the other is interval uncertainty. With the application of the Jensen integral inequality and constructing appropriate Lyapunov–Krasovskii functional based on delay partitioning, several improved delay‐dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Stationary oscillation of interval fuzzy cellular neural networks with mixed delays under impulsive perturbations

In this paper, a class of stationary oscillation of interval fuzzy cellular neural networks (FCNNs) with mixed delays under impulsive perturbations are considered. Mixed delays include discrete time-varying delays and unbounded distributed delays. By establishing a simple Lyapunov function, using impulsive differential inequality techniques and LMI techniques, some new sufficient criteria are obtained to ensure the existence, uniqueness and global exponential stability of stationary oscillation of interval FCNNs. The obtained results can be checked easily by the LMI control toolbox in MATLAB. Moreover, the results obtained in this paper are useful in the application and design of FCNNs, since the sufficient criteria are simple and easy to check in practice. A numerical example is given to illustrate the effectiveness of the obtained result.

State Feedback Stabilization for Neutral-Type Neural Networks with Time-Varying Discrete and Unbounded Distributed Delays

The problem of stabilization for a class of neutral-type neural networks with discrete and unbounded distributed delays is investigated. By introducing an appropriate Lyapunov-Krasovskii functional and using Jensen inequality technique to deal with its derivative, delay-range-dependent and rate-dependent stabilization criteria are presented in the form of LMIs with nonlinear constraints. In order to solve the nonlinear problem, a cone complementarity linearization (CCL) algorithm is offered. In addition, several numerical examples are provided to illustrate the applicability of the proposed approach.

Improved Stability Results for Stochastic Cohen–Grossberg Neural Networks with Discrete and Distributed Delays

This paper is concerned with the exponential stability problem for a class of stochastic Cohen---Grossberg neural networks with discrete and unbounded distributed time delays. By applying the Jensen integral inequality and the generalized Jensen integral inequality, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results.

State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays

This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov–Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results.

Synchronization of switched neural networks with mixed delays via impulsive control

This paper concerns the problem of global exponential synchronization for a class of switched neural networks with time-varying delays and unbounded distributed delays via impulsive control method. By using Lyapunov stability theory, new synchronization criterion is derived. In our synchronization criterion, the switching law can be arbitrary and the concept of average impulsive interval is utilized such that the obtained synchronization criterion is less conservative than those based on maximum of impulsive intervals. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.

An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays

This paper investigates the problem of exponential synchronization of switched stochastic competitive neural networks (SSCNNs) with both interval time-varying delays and distributed delays. The distributed delays can be unbounded or bounded; the stochastic perturbation is of the form of multi-dimensional Brownian motion, and the networks are governed by switching signals with average dwell time. Based on new multiple Lyapunov-Krasovkii functionals, the free-weighting matrix method, Newton-Leibniz formulation, as well as the invariance principle of stochastic differential equations, two sufficient conditions ensuring the exponential synchronization of drive-response SSCNNs are developed. The provided conditions are expressed in terms of linear matrix inequalities, which are dependent on not only both lower and upper bounds of the interval time-varying delays but also delay kernel of unbounded distributed delays or upper bounds for bounded distributed delays. Control gains and average dwell time restricted by given conditions are designed such that they are applicable in practice. Numerical simulations are given to show the effectiveness of the theoretical results.

General criteria for asymptotic and exponential stabilities of neural network models with unbounded delays

For a family of differential equations with infinite delay, we give sufficient conditions for the global asymptotic, and global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Cohen–Grossberg type, with both bounded and unbounded distributed delay, for which general asymptotic and exponential stability criteria are derived. As illustrations, the results are applied to several concrete models studied in the literature, and a comparison of results is given.

Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays

Fuzzy cellular neural network (FCNN) structures are based on the uncertainties in human cognitive processes and in modeling neural systems, and they provide an interface between a human expert and classical cellular neural networks (CNNs). In this paper, an existence and global asymptotic stability analysis of the equilibrium point of FCNNs with time delay in the leakage term and unbounded distributed delays is investigated. Based on the Lyapunov-Krasovskii functional with free-weighting matrix, and using the homeomorphism mapping principle and linear matrix inequalities (LMIs), a new set of stability criteria for FCNNs is obtained with time delay in the leakage term, time-varying delays and unbounded distributed delays. The proposed results can be easily checked via the LMI Control Toolbox in MATLAB. Moreover, it is well known that the stability behavior of FCNNs is very sensitive to the time delay in the leakage term. In the absence of the leakage term, a new stability criterion is also derived by employing a Lyapunov-Krasovskii functional using an LMI approach. Numerical examples are provided to illustrate the effectiveness and reduced conservativeness of the developed techniques.