Abstract: In this paper, reliable consensus of multi-agent systems
with sampled-data is investigated. By using a suitable
Lyapunov-Krasovskii functional and some techniques such as
Wirtinger Inequality, Schur Complement and Kronecker Product, the
results of such system are obtained by solving a set of Linear Matrix
Inequalities (LMIs). One numerical example is included to show the
effectiveness of the proposed criteria.
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, together with some improved
Lyapunov-Krasovskii functional and effective mathematical
techniques, several sufficient conditions are derived to guarantee the
error system is globally asymptotically stable with H∞
performance, in which both the time-delay and its time variation
can be fully considered. In order to get less conservative results of
the state estimation condition, zero equalities and reciprocally
convex approach are employed. The estimator gain matrix can be
obtained in terms of the solution to linear matrix inequalities. A
numerical example is provided to illustrate the usefulness and
effectiveness of the obtained 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: 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.
Abstract: In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.
Abstract: This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.
Abstract: This paper presents the robust stability criteria for uncertain genetic regulatory networks with time-varying delays. One key point of the criterion is that the decomposition of the matrix ˜D into ˜D = ˜D1 + ˜D2. This decomposition corresponds to a decomposition of the delayed terms into two groups: the stabilizing ones and the destabilizing ones. This technique enables one to take the stabilizing effect of part of the delayed terms into account. Meanwhile, by choosing an appropriate new Lyapunov functional, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs). Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.
Abstract: This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.
Abstract: In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.
Abstract: This paper considers H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.