Abstract: The reachable set bounding estimation for distributed
delay systems with disturbances is a new problem. In this paper,we
consider this problem subject to not only time varying delay and
polytopic uncertainties but also distributed delay systems which is
not studied fully untill now. we can obtain improved non-ellipsoidal
reachable set estimation for neural networks with time-varying delay
by the maximal Lyapunov-Krasovskii fuctional which is constructed
as the pointwise maximum of a family of Lyapunov-Krasovskii
fuctionals corresponds to vertexes of uncertain polytope.On the other
hand,matrix inequalities containing only one scalar and Matlabs
LMI Toolbox is utilized to give a non-ellipsoidal description of the
reachable set.finally,numerical examples are given to illustrate the
existing results.
Abstract: This paper is concerned with the stability problem
with two additive time-varying delay components. By choosing one
augmented Lyapunov-Krasovskii functional, using some new zero
equalities, and combining linear matrix inequalities (LMI)
techniques, two new sufficient criteria ensuring the global stability
asymptotic stability of DNNs is obtained. These stability criteria are
present in terms of linear matrix inequalities and can be easily
checked. Finally, some examples are showed to demonstrate the
effectiveness and less conservatism of the proposed method.
Abstract: In this paper, the design problem of state estimator for
neural networks with the mixed time-varying delays are investigated
by constructing appropriate Lyapunov-Krasovskii functionals and
using some effective mathematical techniques. In order to derive
several conditions to guarantee the estimation error systems to be
globally exponential stable, we transform the considered systems
into the neural-type time-delay systems. Then with a set of linear
inequalities(LMIs), we can obtain the stable criteria. Finally, three
numerical examples are given to show the effectiveness and less
conservatism of the proposed criterion.
Abstract: This paper deals with the problem of delay-dependent
stability for neural networks with distributed delays. Some new
sufficient condition are derived by constructing a novel
Lyapunov-Krasovskii functional approach. The criteria are
formulated in terms of a set of linear matrix inequalities, this is
convenient for numerically checking the system stability using the
powerful MATLAB LMI Toolbox. Moreover, in order to show the
stability condition in this paper gives much less conservative results
than those in the literature, numerical examples are considered.
Abstract: This paper studies the problem of asymptotically
stability for neural networks with time-varying delays.By establishing
a suitable Lyapunov-Krasovskii function and several novel sufficient
conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.
Abstract: This paper studies the problem of stability criteria
for neural networks with two additive time-varying delays.A new
Lyapunov-Krasovskii function is constructed and some new delay
dependent stability criterias are derived in the terms of linear
matrix inequalities(LMI), zero equalities and reciprocally convex
approach.The several stability criterion proposed in this paper is
simpler and effective. Finally,numerical examples are provided to
demonstrate the feasibility and effectiveness of our results.
Abstract: In this paper, a stochastic predator-prey system with Bedding-DeAngelis functional response is studied. By constructing a suitable Lyapunov founction, sufficient conditions for species to be stochastically permanent is established. Meanwhile, we show that the species will become extinct with probability one if the noise is sufficiently large.
Abstract: This paper deals with the problem of stability of
neural networks with leakage, discrete and distributed delays. A
new Lyapunov functional which contains some new double integral
terms are introduced. By using appropriate model transformation
that shifts the considered systems into the neutral-type time-delay
system, and by making use of some inequality techniques,
delay-dependent criteria are developed to guarantee the stability of
the considered system. Finally, numerical examples are provided to
illustrate the usefulness of the proposed main results.
Abstract: In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and
discrete delays has been investigated. Some new sufficient condition
are derived based on a novel Lyapunov-Krasovskii functional
approach. These new criteria based on delay partitioning idea are
proved to be less conservative because free-weighting matrices
method and a convex optimization approach are considered. Finally,
one numerical example is given to illustrate the the usefulness and
feasibility of the proposed main results.
Abstract: This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.
Abstract: This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.
Abstract: In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.
Abstract: In this paper,the exponential passivity criteria for BAM neural networks with time-varying delays is studied.By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments,a novel sufficient condition is established to guarantee the exponential stability of the considered system.Finally,a numerical example is provided to illustrate the usefulness of the proposed main results
Abstract: Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.
Abstract: In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of
positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.
Abstract: The problems of globally exponential stability and dissipativity analysis for static neural networks (NNs) with time delay is investigated in this paper. Some delay-dependent stability criteria are established for static NNs with time delay using the delay partitioning technique. In terms of this criteria, the delay-dependent sufficient condition is given to guarantee the dissipativity of static NNs with time delay. All the given results in this paper are not only dependent upon the time delay but also upon the number of delay partitions. Two numerical examples are used to show the effectiveness of the proposed methods.
Abstract: In this paper, a stochastic predator-prey system with Holling II functional response is studied. First, we show that there is a unique positive solution to the system for any given positive initial value. Then, stochastically bounded of the positive solution to the stochastic system is derived. Moreover, sufficient conditions for global asymptotic stability are also established. In the end, some simulation figures are carried out to support the analytical findings.
Abstract: This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.
Abstract: In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Abstract: This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.