Abstract: Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.
Abstract: Financial inclusion has become a crucially important
factor in debates on economic inequality posing challenges to the
financial systems of countries around the world. Nowadays
governments and banks are concerned about creating products that
allow access to wide sectors of the population. The creation of
banking products by the financial sector for people with low incomes
tends to lead to improvements in the quality of life of vulnerable parts
of the population. In countries with notable social and economic
inequalities, financial inclusion is a key aspect for equitable
economic growth. This study is based on the case of Colombia, which is a country
with a strong record of economic growth over the past decade.
Nevertheless, corruption, unemployment, and poverty contribute to
uncertainty regarding the country’s future growth prospects. This study wants to explain the situation of financial exclusion and
financial inclusion with respect to the Colombian case. Financial
inclusion is going to be studied from the perspective of social
innovation.
Abstract: Sampled-data controller is presented for solid oxide
fuel cell systems which is expressed by a sector bounded nonlinear
model. The proposed control law is obtained by solving a convex
problem satisfying several linear matrix inequalities. Simulation
results are given to show the effectiveness of the proposed design
method.
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 author introduced the integral operator , by using this
operator a new subclasses of analytic functions are introduced. For
these classes, several Fekete-Szeg¨ type coefficient inequalities are
obtained.
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 deals with the problem of passivity
analysis for stochastic neural networks with leakage, discrete and
distributed delays. By using delay partitioning technique, free
weighting matrix method and stochastic analysis technique, several
sufficient conditions for the passivity of the addressed neural
networks are established in terms of linear matrix inequalities
(LMIs), in which both the time-delay and its time derivative can be
fully considered. A numerical example is given to show the
usefulness and effectiveness of the obtained 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 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: The study aimed to investigate whether the affect (experience of feeling or emotion) of ethnic minority people can be predicted by gender and marital status. Toward this end, positive affect and negative affect of 103 adult indigenous persons were measured. Analysis of data in multiple regressions demonstrated that both gender and marital status are significantly associated with positive affect (Gender: β=.318, p
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, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.
Abstract: Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.
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: In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.
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 examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.