synchronization of chaotic lur e systems with time delays using sampled data control the asymptotical synchronization problem is investigated for two identical chaotic lur e systems with time delays the sampled data control method is employed for the system design a new synchronization condition is proposed in the form of linear matrix inequalities the error system is shown to be asymptotically stable with the constructed new piecewise differentiable lyapunov krasovskii functional lkf different from the existing work the new lkf makes full use of the information in the nonlinear part of the system the obtained stability condition is less conservative than some of the existing ones a longer sampling period is achieved with the new method the numerical examples are given and the simulations are performed on chua s circuit the results show the superiorities and effectiveness of the proposed control method

extended dissipative analysis for neural networks with time varying delays in this brief an extended dissipativity analysis was conducted for a neural network with time varying delays the concept of the extended dissipativity can be used to solve for the h l2 l passive and dissipative performance by adjusting the weighting matrices in a new performance index in addition the activation function dividing method is modified by introducing a tuning parameter examples are provided to show the effectiveness and less conservatism of the proposed method

reliable asynchronous sampled data filtering of t s fuzzy uncertain delayed neural networks with stochastic switched topologies abstract this paper investigates the issue of the reliable asynchronous sampled data filtering of takagi sugeno t s fuzzy delayed neural networks with stochastic intermittent faults randomly occurring time varying parameters uncertainties and controller gain fluctuation the asynchronous phenomenon occurs between the system modes and controller modes first in order to reduce the utilization rate of communication bandwidth a novel alterable sampled data terminal method is considered via variable sampling rates second based on the fuzzy model based control approach improved reciprocally convex inequality and new parameter time dependent discontinuous lyapunov approach several relaxed conditions are derived and compared with the existing work third the intermittent fault tolerance scheme is also taken into fully account in designing a reliable asynchronous sampled data controller which ensures such that the resultant neural networks is asymptotically stable finally two numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

further results on exponential stability of neural networks with time varying delay this paper investigates the problem of the exponential stability for a class of neural networks with time varying delay a triple integral term and a term considering the delay information in a new way are introduced to the lyapunov krasovskii functional lkf the obtained criterion show advantages over the existing ones since not only a novel lkf is constructed but also several techniques such as wirtinger based inequality and convex combination technique are used to estimate the upper bound of the derivative of the lkf finally a numerical example is provided to verify the effectiveness and benefit of the proposed criterion

the bm l _ mathbf 1 norm density estimator process the notion of an l1 norm density estimator process indexed by a class of kernels is introduced then a functional central limit theorem and a glivenko cantelli theorem are established for this process while assembling the necessary machinery to prove these results a body of poissonization techniques and restricted chaining methods is developed which is useful for studying weak convergence of general processes indexed by a class of functions none of the theorems imposes any condition at all on the underlying lebesgue density f also somewhat unexpectedly the distribution of the limiting gaussian process does not depend on f

an improved result on reachable set estimation and synthesis of time delay systems in this paper the problems of reachable set estimation and synthesis of time delay systems are investigated by introducing the non uniform delay partitioning method and the triple integral technique an improved reachable set estimation condition is proposed in terms of linear matrix inequality based on the criterion a sufficient condition for the existence of a state feedback controller is established to render the reachable set of the closed loop system be bounded by a given ellipsoid two numerical examples are given to demonstrate the effectiveness of the obtained results

exponential synchronization of chaotic neural networks with time varying delay via intermittent output feedback approach abstract this paper is dealt with the problem of exponential synchronization for chaotic neural networks with time varying delay by using intermittent output feedback control based on the lyapunov krasovskii functional method and the lower bound lemma for reciprocally convex technique a novel criterion for existence of the controller is first established to ensure synchronization between the master and slave systems moreover from the delay point of view the derived criterion is extended to the relaxed case because of introducing an adjustable parameter in the lyapunov krasovskii functional finally a numerical simulation is carried out to demonstrate the effectiveness of the proposed synchronization law

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

properties of a job search problem on a partially observable markov chain in a dynamic economy this paper observes a job search problem on a partially observable markov chain which can be considered as an extension of a job search in a dynamic economy in 1 this problem is formulated as the state changes according to a partially observable markov chain i e the current state cannot be observed but there exists some information regarding what a present state is all information about the unobservable state are summarized by the probability distributions on the state space and we employ the bayes theorem as a learning procedure the total positivity of order two or simply tp 2 is a fundamental property to investigate sequential decision problems and it also plays an important role in the bayesian learning procedure for a partially observable markov process by using this property we consider some relationships among prior and posterior information and the optimal policy we will also observe the probabilities to make a transition into each state after some additional transitions by empolying the optimal policy in the stock market suppose that the states correspond to the business situation of one company and if there is a state designating the default then the problem is what time the stocks are sold off before bankrupt and the probability to become bankrupt will be also observed

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities in this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables the results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions e g the multivariate t and wishart distributions inequalities of this type yield bounds for multivariate confidence set probabilities

large time asymptotics in contaminant transport in porous media in this paper we derive large time solutions of the partial differential equations modelling contaminant transport in porous media for initial data with bounded support while the main emphasis is on two space dimensions for the sake of completeness we give a brief summary of the corresponding results for one space dimension the philosophy behind the paper is to compare the results of a formal asymptotic analysis of the governing equations as t to infty with numerical solutions of the complete initial value problem the analytic results are obtained using the method of dominant balance which identifies the dominant terms in the model equations determining the behaviour of the solution in the large time limit these are found in terms of time scaled space similarity variables and the procedure results in a reduction of the number of independent variables in the original partial differential equation this generates what we call a reduced equation the solution of which depends crucially on the value

an improved sequentially rejective bonferroni test procedure complexity these procedures can be used whenever the observed levels of significance are available for all individual tests it is shown that both the holm and shaffer procedures can be improved under the assumption of positive orthant dependence for the test statistics it is noted that this assumption is met in many important practical situations and recommended that in these cases the new procedure be used in place of its predecessors whenever the required observed significance levels are available the methodology is illustrated with a numerical example

stochastic finite time h state estimation for discrete time semi markovian jump neural networks with time varying delays in this article the finite time h infty state estimation problem is addressed for a class of discrete time neural networks with semi markovian jump parameters and time varying delays the focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite time bounded with a prescribed h infty performance level via finite time lyapunov stability theory by constructing a delay product type lyapunov functional in which the information of time varying delays and characteristics of activation functions are fully taken into account and using the jensen summation inequality the free weighting matrix approach and the extended reciprocally convex matrix inequality some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator finally numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results

on reachable sets for positive linear systems under constrained exogenous inputs this paper focuses on positive linear time invariant systems with constant coefficients and specific exogenous disturbance the problem of finding a hyper pyramid to bound the set of the states that are reachable from the origin in the euclidean space is addressed subject to inputs whose 1 1 norm or 1 norm is bounded by a prescribed constant the lyapunov approach is applied and a bounding hyper pyramid is obtained by solving a set of inequalities iterative procedures with an adjustable parameter for reducing the hyper volume of the bounding hyper pyramid for the reachable set are proposed

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

new stability criteria of neural networks with interval time varying delay a piecewise delay method abstract this paper provides improved conditions for the global asymptotic stability of a class of neural networks with interval time varying delays a piecewise delay method is firstly proposed in this method the variation interval of the time delay is divided into two subintervals by introducing its central point then by constructing a new lyapunov krasovskii functional and checking its variation in the two subintervals respectively some new delay dependent stability criteria for the addressed neural networks are derived numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature

estimation of domain of attraction for aperiodic sampled data switched delayed neural networks subject to actuator saturation in this paper for the case of the asynchronous switching caused by that subsystem s switching occuring during a sampling interval the domain of attraction estimation problem is investigated for aperiodic sampled data switched delayed neural networks asdsdnns subject to actuator saturation a parameters dependent time scheduled lyapunov functional consisting of a novel looped functional is constructed using segmentation technology and linear interpolation by employing this novel functional and using an average dwell time adt approach exponential stability criteria are proposed for polytopic uncertain asdsdnns subject to actuator saturation and a relationship between adt and sampling period is revealed for asdsdnns as a corollary exponential stability criteria are proposed for nominal asdsdnns subject to actuator saturation furthermore by describing the domain of attraction as a time varying ellipsoid determined by the time scheduled lyapunov matrix the proposed theoretical conditions are transformed into a linear matrix inequality lmi based multi objective optimization problem the dynamic estimates of the domain of attraction for asdsdnns are solved numerical simulation examples are provided to illustrate the effectiveness of the proposed method

technical communique further result on reachable set bounding for linear uncertain polytopic systems with interval time varying delays the problem of reachable set estimation of linear uncertain polytopic time varying delay systems subject to bounded peak inputs is studied in this paper the delays considered in this paper are assumed to be non differentiable and vary within an interval where the lower and upper bounds are known based on the lyapunov krasovskii method and delay decomposition technique a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one dimensional search method and matlab s lmi toolbox and allow us to find the smallest radius a numerical example is given to illustrate the effectiveness of the proposed result

extended dissipativity analysis for markovian jump neural networks with time varying delay via delay product type functionals this paper investigates the problem of extended dissipativity for markovian jump neural networks mjnns with a time varying delay the objective is to derive less conservative extended dissipativity criteria for delayed mjnns toward this aim an appropriate lyapunov krasovskii functional lkf with some improved delay product type terms is first constructed then by employing the extended reciprocally convex matrix inequality ercmi and the wirtinger based integral inequality to estimate the derivative of the constructed lkf a delay dependent extended dissipativity condition is derived for the delayed mjnns an improved extended dissipativity criterion is also given via the allowable delay sets method based on the above mentioned results the extended dissipativity condition of delayed nns without markovian jump parameters is directly derived finally three numerical examples are employed to illustrate the advantages of the proposed method

on global dissipativity of nonautonomous neural networks with multiple proportional delays this brief addresses the problem of global dissipativity analysis of nonautonomous neural networks with multiple proportional delays by using a novel constructive approach based on some comparison techniques for differential inequalities new explicit delay independent conditions are derived using m matrix theory to ensure the existence of generalized exponential attracting sets and the global dissipativity of the system the method presented in this brief is also utilized to derive a generalized exponential estimate for a class of halanay type inequalities with proportional delays finally three numerical examples are given to illustrate the effectiveness and improvement of the obtained results

a time dependent hamilton jacobi formulation of reachable sets for continuous dynamic games we describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game the algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time dependent hamilton jacobi isaacs partial differential equation while alternative techniques for computing the reachable set have been proposed the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters because the time dependent equation s solution is continuous and defined throughout the state space methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions a numerical implementation of our formulation is described and has been released on the web its correctness is verified through a two vehicle three dimensional collision avoidance example for which an analytic solution is available

technical communique on reachable sets for linear systems with delay and bounded peak inputs linear systems with constant coefficients and time varying delays are considered we address the problem of finding an ellipsoid that bounds the set of the states in the euclidean space that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar the system may encounter uncertainties in the matrices of its state space model and in the delay length the lyapunov razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper bound of the delay length

the three dimensional gaussian product inequality abstract we prove the 3 dimensional gaussian product inequality i e for any real valued centered gaussian random vector x y z and m n it holds that e x 2 m y 2 m z 2 m e x 2 m e y 2 m e z 2 m this settles positively the gaussian product conjecture in the 3 dimensional case our proof is based on some improved inequalities on multi term products involving 2 dimensional gaussian random vectors the improved inequalities are derived using the gaussian hypergeometric functions and are of independent interest as by products several new combinatorial identities and inequalities are obtained

exponential stabilization of non autonomous delayed neural networks via riccati equations this paper concerns with the problem of exponential stabilization for a class of non autonomous neural networks with mixed discrete and distributed time varying delays two cases of discrete time varying delay namely i slowly time varying and ii fast time varying are considered by constructing an appropriate lyapunov krasovskii functional in case i and utilizing the razumikhin technique in case ii we establish some new delay dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed loop system the proposed conditions are derived through solutions of some types of riccati differential equations applications to control a class of autonomous neural networks with mixed time varying delays are also discussed in this paper some numerical examples are provided to illustrate the effectiveness of the obtained results

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

generalized jensen inequalities with application to stability analysis of systems with distributed delays over infinite time horizons the jensen inequality has been recognized as a powerful tool to deal with the stability of time delay systems recently a new inequality that encompasses the jensen inequality was proposed for the stability analysis of systems with finite delays in this paper we first present a generalized integral inequality and its double integral extension it is shown how these inequalities can be applied to improve the stability result for linear continuous time systems with gamma distributed delays then for the discrete time counterpart we provide an extended jensen summation inequality with infinite sequences which leads to less conservative stability conditions for linear discrete time systems with poisson distributed delays the improvements obtained by the introduced generalized inequalities are demonstrated through examples

asymptotics in the critical case for whitham type equations abstract consider the cauchy problem for nonlinear dissipative evolution equations u t n u u l u 0 x r t 0 u 0 x u 0 x x r where l is the linear pseudodifferential operator l u f x l u and the nonlinearity is a quadratic pseudodifferential operator n u u f x r a t y u t y u t y d y u f x u is direct fourier transformation let the initial data u 0 h 0 h 0 1 2 are sufficiently small and have a non zero total mass m u 0 x d x 0 here h n m l 2 x m i x n x l 2 is the weighted sobolev space then we prove that the main term of the large time asymptotics of solutions in the critical case is given by the self similar solution defined uniquely by the total mass m of the initial data

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

some novel approaches on state estimation of delayed neural networks this paper studies the issue of state estimation for a class of neural networks nns with time varying delay a novel lyapunov krasovskii functional lkf is constructed where triple integral terms are used and a secondary delay partition approach sdpa is employed compared with the existing delay partition approaches the proposed approach can exploit more information on the time delay intervals by taking full advantage of a modified wirtinger s integral inequality mwii improved delay dependent stability criteria are derived which guarantee the existence of desired state estimator for delayed neural networks dnns a better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities lmis in addition a new activation function dividing method is developed by bringing in some adjustable parameters three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods

global asymptotic stability for delayed neural networks using an integral inequality based on nonorthogonal polynomials this brief is concerned with global asymptotic stability of a neural network with a time varying delay first by introducing an auxiliary vector with some nonorthogonal polynomials a slack matrix based integral inequality is established which includes some existing one as its special case second a novel lyapunov krasovskii functional is constructed to suit for the use of the obtained integral inequality as a result a less conservative stability criterion is derived whose effectiveness is finally demonstrated through two well used numerical examples

asymptotic profiles for covection diffusion equations with variable diffusion abstract we investigate the large time behavior of solutions of the convection diffusion equation u t div a x u d u q 1 u d r n in 0 r n with integrable initial data u0 x we take a x 1 b x 0 with b smooth and decaying to zero fast enough as x when q 1 1 n it is known that the solutions behave in a first approximation like the solutions of the head equation taking the same initial data as t we show here the influence of the nonlinear term and the variable diffusion in the large time behavior by obtaining the second term in the asymptotic development of solutions as t

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

dissipativity analysis for discrete time stochastic neural networks with time varying delays in this paper the problem of dissipativity analysis is discussed for discrete time stochastic neural networks with time varying discrete and finite distributed delays the discretized jensen inequality and lower bounds lemma are adopted to deal with the involved finite sum quadratic terms and a sufficient condition is derived to ensure the considered neural networks to be globally asymptotically stable in the mean square and strictly q s r y dissipative which is delay dependent in the sense that it depends on not only the discrete delay but also the finite distributed delay based on the dissipativity criterion some special cases are also discussed compared with the existing ones the merit of the proposed results in this paper lies in their reduced conservatism and less decision variables three examples are given to illustrate the effectiveness and benefits of our theoretical results

state feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties abstract this study examines the synchronization problem of impulsive neural networks with mixed time varying delays and linear fractional uncertainties the mixed time varying delays include distributed leakage discrete and distributed time varying delays moreover the restrictions on derivatives of time varying delays with upper bounds to smaller than one is relaxed by introducing free weight matrices based on suitable lyapunov krasovskii functionals and integral inequalities linear matrix inequality approach is used to derive the sufficient conditions that guarantee the synchronization criteria of impulsive neural networks via delay dependent state feedback control finally three numerical examples are given to show the effectiveness of the theoretical results

non fragile memory filtering of t s fuzzy delayed neural networks based on switched fuzzy sampled data control abstract this paper deals with the non fragile memory filtering issue of t s fuzzy delayed neural networks with randomly occurring time varying parameters uncertainties and variable sampling rates compared with existing sampled data control schemes an improved switched fuzzy memory sampled data control protocol is designed for the first time which involves not only a signal transmission delay but also switched topologies by developing some new terms and taking full advantage of the variable characteristics related to the actual sampling pattern a modified loose looped fuzzy membership functions fmfs dependent lyapunov krasovskii functional lkf is constructed based on the information of the time derivative of fmfs meanwhile some relaxed matrices chosen in lkf are not consequentially positive definite moreover with the lkf methodology and employing the developed estimation technique several optimized control algorithms with both a larger sampling period and upper bound of time varying delays for achieving the stabilization of the resultant t s fuzzy delayed neural networks are derived finally a numerical example is presented to demonstrate the superiority and applicability of the theoretical results

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

static output feedback stabilization necessary conditions for multiple delay controllers this note focuses on the static output feedback stabilization problem for a class of single input single output systems when the control law includes multiple distinct delays we are interested in giving necessary conditions for the existence of such stabilizing controllers illustrative examples second order system chain of integrators or chain of oscillators are presented and discussed

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

m matrices as covariance matrices of multinormal distributions abstract the class of multivariate normal densities n 0 whose inverse covariance matrix 1 is an m matrix is equivalent to this normal density being multivariate totally positive of order 2 mtp 2 equivalent characterizations are given in terms of certain partial correlation coefficients being positive it is further shown that related partial and multiple regression coefficients and canonical correlation are positive when is an m matrix the corresponding normal random vector components are negatively associated this concept and some extensions are discussed

extended dissipativity and control synthesis of interval type 2 fuzzy systems via line integral lyapunov function this article addresses the problems of the stability and extended dissipativity analysis and control synthesis for interval type 2 fuzzy systems a sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established by using line integral lyapunov function this condition obtained is more general than the one which is based on quadratic lyapunov function calculating the control gains in light of the obtained condition is more complicated and challenging since the matrix inequalities in the condition are of nonlinear form with respect to some matrix variables also change of variable as well as the existing matrix decoupling approach cannot be used directly to handle the nonlinear problem by utilizing cone complementarity linearization algorithm and a new matrix decoupling method the state feedback controller can be developed by converting the nonlinear matrix inequalities into a quadratic optimization problem with linear inequality constraints four simulation examples are provided to show the effectiveness of the proposed approach

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

on the reachable set bounding of uncertain dynamic systems with time varying delays and disturbances in this paper improved conditions are proposed for finding an ellipsoidal bound of reachable sets which bound the state trajectories of uncertain dynamic systems with time varying delays and bounded peak disturbances a more generalized time derivative condition is considered in comparison with previous work by the use of convex hull properties and application of the lyapunov method sufficient conditions for finding an ellipsoidal bound of reachable sets of the concerned systems are established in terms of linear matrix inequalities lmis two numerical examples are included to show the superiority and effectiveness of our results

exponential stability and extended dissipativity criteria for generalized discrete time neural networks with additive time varying delays abstract this paper is concerned with exponential stability and extended dissipativity criteria for generalized discrete time neural networks gdnns with additive time varying delays the generalized dissipativity analysis combines a few previous results into a framework such as l 2 l performance h performance passivity performance strictly q s r dissipative and strictly q s r dissipative the definition of exponential stability for gdnns is given with a new and more appropriate expression a novel augmented lyapunov krasovskii functional lkf which involves more information about the additive time varying delays is constructed by introducing more zero equalities and using a new double summation inequality together with finsler s lemma an improved delay dependent exponential stability and extended dissipativity criterion are derived in terms of convex combination technique cct finally numerical examples are given to illustrate the usefulness and advantages of the proposed methods

decentralized adaptive delay dependent neural network control for a class of large scale interconnected nonlinear systems this paper investigates the problem of adaptive decentralized control for a class of large scale interconnected nonlinear systems with unknown time delays and the unmeasured states compared with the existing results the delay parameters are estimated by utilizing mean value theorem and adaptive mechanism with the help of the delay estimations a delay dependent state observer is designed to make the states available based on lyapunov stability theorem and the backstepping technique the novel adaptive neural network memory output feedback controllers are developed it is proved that the proposed control scheme can guarantee that all the signals in the closed loop system are bounded and the tracking error converges to the adjustable neighborhood of the origin the effectiveness of the proposed control scheme is illustrated by the simulation results

novel delay dependent master slave synchronization criteria of chaotic lur e systems with time varying delay feedback control this paper is concerned with the issue of master slave synchronization for chaotic lur e systems clss with time varying delay feedback control a novel integral inequality is developed by employing two adjustable parameters which encompasses the celebrated wirtinger s integral inequality and jensen s inequality as two special cases by constructing an augmented lyapunov krasovskii functional lkf taking fully the information time varying delay range into account less conservative delay dependent synchronization criteria are established in the form of linear matrix inequalities lims besides the desired controller gain can be achieved by introducing new nonlinear function conditions which have not been proposed so far finally a numerical example of typical chua s circuit is presented to show the improvements over the existing criteria and the effectiveness of the design approach

a new approach to state bounding for linear time varying systems with delay and bounded disturbances abstract in this note the problem of state bounding for linear time varying systems with delay and bounded disturbances input is considered for the first time by using a novel approach which does not involve the lyapunov krasovskii functional method new explicit delay independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it a numerical example is given to illustrate the effectiveness of the obtained result

validity of the hochberg procedure revisited for clinical trial applications there is much interest in using the hochberg procedure hp for statistical tests on primary endpoints of confirmatory clinical trials the procedure is simple to use and enjoys more power than the bonferroni and the holm procedures however the hp is not assumption free like the other two procedures it controls the familywise type i error rate when test statistics used for statistical tests are independent or if dependent satisfy a conditionally independent formulation otherwise its properties for dependent tests at present are not fully understood consequently its use for confirmatory trials especially for their primary endpoints remains worrisome confirmatory trials are typically designed with 1 2 primary endpoints therefore a question was raised at the food and drug administration as to whether the hp is a valid test for the simple case of performing treatment to control comparisons on two primary endpoints when their test statistics are not independent confirmatory trials for statistical tests normally use simple test statistics such as the normal z student s t and chi square the literature does include some work on the hp for dependent cases covering these test statistics but concerns remain regarding its use for confirmatory trials for which endpoint tests are mostly of the dependent kind the purpose of this paper is therefore to revisit this procedure and provide sufficient details for better understanding of its performance for dependent cases related to the aforementioned question published 2015 this article is a u s government work and is in the public domain in the usa

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

a new method of reachable set estimation for time delay systems with polytopic uncertainties we address the reachable set bounding problem of linear systems subject to both time varying delay and polytopic uncertainties a novel criterion is established to give a more accurate description of the set which bounds the states starting from the origin by inputs with peak values by combining the maximal lyapunov functional and the reciprocally convex approach we obtain a tighter reachable set estimation with lower computational complexity the corresponding reachable set condition for the common lyapunov functional can be obtained naturally as a special case of the above result finally two examples illustrate the advantages of our proposed method

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

consensus rate regulation for general linear multi agent systems under directed topology recently optimization in distributed multi agent coordination has been studied concerning convergence speed the optimal convergence speed of consensus for multi agent systems consisting of general linear node dynamics is still an open problem this paper aims to design optimal distributed consensus protocols for general identical linear continuous time cooperative systems which not only minimize some local quadric performances but also regulate the consensus rate including convergence rate and damping rate for the multi agent systems the graph topology is assumed to be fixed and directed the inverse optimal design method is utilized and the resulting optimal distributed protocols place part of close loop poles of the global disagreement systems at specified locations asymptotically while the remains far from the imaginary axis enough it turns out that for the identical linear continuous time multi agent systems the convergence speed has no upper bound the main advantages of the developed method over the lqr design method are that the resulting multi agent systems can achieve specified consensus rate asymptotically and the resulting protocols have the whole right half complex plane as its asymptotical consensus region numerical examples are given to illustrate the effectiveness of the proposed design procedures

truncated simes tests it is known that the one sided simes test controls the error rate if the underlying distribution is multivariate totally positive of order 2 mtp2 but not in general the two sided test also controls the error rate when the coordinate absolute value has an mtp2 distribution which holds more generally we prove mathematically that when the coordinate absolute value controls the error rate at level 2 then certain kinds of truncated simes tests also control the one sided error rate at level we also compare the closure of the truncated tests with the holms hochberg and hommel procedures in many scenarios when the test statistics are multivariate normal

direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete unbounded distributed delays and markovian jumping parameters in this paper the problem of synchronization of chaotic fuzzy cellular neural networks fcnns with discrete unbounded distributed delays and markovian jumping parameters mjps is investigated sufficient delay dependent stability criteria are obtained in terms of linear matrix inequalities lmis to ensure the chaotic delayed fcnns to be stochastic asymptotically synchronous with the help of free weighting matrix and some inequality techniques the information of the delayed plant states can be taken into full consideration here the delay interval is decomposed into two subintervals by using the tuning parameter such that 0 1 by developing a delay decomposition approach and constructing suitable lyapunov krasovskii functional lkf sufficient conditions for synchronization are established for each subinterval numerical example and its simulations are provided to demonstrate the effectiveness and less conservatism of the derived results

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

hochberg s step up method cutting corners off holm s step down method holm s method and hochberg s method for multiple testing can be viewed as step down and step up versions of the bonferroni test we show that both are special cases of partition testing the difference is that while holm s method tests each partition hypothesis using the largest order statistic setting a critical value based on the bonferroni inequality hochberg s method tests each partition hypothesis using all the order statistics setting a series of critical values based on simes inequality geometrically hochberg s step up method cuts corners off the acceptance regions of holm s step down method by making assumptions on the joint distribution of the test statistics as can be expected partition testing making use of the joint distribution of the test statistics is more powerful than partition testing using probabilistic inequalities thus if the joint distribution of the test statistics is available through modelling for example we recommend partition step down testing setting exact critical values based on the joint distribution

path weights in concentration graphs a graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph relevant features of the distribution are represented by vertices edges and other higher order graphical structures such as cliques or paths typically paths play a central role in these models because they determine the independence relationships among variables however while a theory of path coefficients is available in models for directed graphs little has been investigated about the strength of the association represented by a path in an undirected graph essentially it has been shown that the covariance between two variables can be decomposed into a sum of weights associated with each of the paths connecting the two variables in the corresponding concentration graph in this context we consider concentration graph models and provide an extensive analysis of the properties of path weights and their interpretation more specifically we give an interpretation of covariance weights through their factorisation into a partial covariance and an inflation factor we then extend the covariance decomposition over the paths of an undirected graph to other measures of association such as the marginal correlation coefficient and a quantity that we call the inflated correlation the usefulness of these findings is illustrated with an application to the analysis of dietary intake networks

design of extended dissipativity state estimation for generalized neural networks with mixed time varying delay signals this paper investigates the issue of extended dissipativity state estimation of generalized neural networks gnns with mixed time varying delay signals the integral terms in the time derivative of the lyapunovkrasovskii functionals lkfs are estimated by the famous jensens inequality reciprocally convex combination rcc approach together with the wirtinger double integral inequality wdii technique in addition in order to estimate the double integral terms in the derivative of the lkf a new integral inequality is proposed as a result a new delay dependent criterion is derived under which the estimated error system is extended dissipative the concept of extended dissipativity state estimation can be applied to deal with the l2l state estimation h state estimation passivity state estimation mixed h and passivity state estimation q s r dissipativity state estimation of gnns by choosing the weighting matrices the advantage of the proposed method is demonstrated by five numerical examples among them one example was supported by real life application of the benchmark problem that is associated with reasonable issues in the sense of an extended dissipativity performance

non exchangeable copulas and multivariate total positivity multivariate total positivity of order 2 mtp2 is a dependence property with a number of applications in statistics and mathematics given the theoretical and practical relevance of mtp2 it is important to investigate the conditions under which random vectors have this property in this paper we contribute to the development of the theory of stochastic dependence by employing the general concept of copula in particular we propose a new family of non exchangeable archimedean copulas which leads to mtp2 the focus on non exchangeability allows us to overcome the limitations induced by symmetric dependence typical of standard archimedean copulas

stability and l_ 2 performance analysis of stochastic delayed neural networks this brief focuses on the robust mean square exponential stability and l2 performance analysis for a class of uncertain time delay neural networks perturbed by both additive and multiplicative stochastic noises new mean square exponential stability and l2 performance criteria are developed based on the delay partition lyapunov krasovskii functional method and generalized finsler lemma which is applicable to stochastic systems the analytical results are established without involving any model transformation estimation for cross terms additional free weighting matrices or tuning parameters numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones

sampled data control for a class of linear time varying systems this paper is concerned with the sampled data control for a class of linear time varying system a classic halanay inequality is first extended to the time varying sampled data system then based on the comparison principle and the extended halanay inequality new criteria for globally uniformly exponential stability and globally uniformly asymptotic stability of the corresponding closed loop system are derived furthermore an algorithm is presented to solve the gain synthesis problem finally one example is given to show the effectiveness of the obtained results

extended dissipativity analysis for discrete time delayed neural networks based on an extended reciprocally convex matrix inequality abstract in this paper the extended dissipativity analysis for discrete time neural networks with a time varying delay is investigated first a novel lyapunov krasovskii functional lkf is constructed with a delay product type term introduced then in the forward difference of the lkf the sum terms are bounded via an extended reciprocally convex matrix inequality as a result an extended dissipativity criterion is established in terms of linear matrix inequalities meanwhile this criterion is extended to the stability analysis of the counterpart system without disturbance finally two numerical examples are given to demonstrate the effectiveness and improvements of the presented criterion

new admissibility analysis for discrete singular systems with time varying delay in this paper the issue of admissibility for discrete singular systems with time varying delay is addressed the main contribution of this paper is to reduce the conservatism of the considered system by adopting an improved reciprocally convex combination approach to bound the forward difference of the double summation term and utilizing the reciprocally convex combination approach to bound the forward difference of the triple summation term in the lyapunov function without employing decomposition and equivalent transformation of the considered system a strict delay dependent linear matrix inequality lmi criterion is built to guarantee the considered system to be regular causal and stable a numerical example is given to illustrate the effectiveness of this proposed method

finite time stability of a class of non autonomous neural networks with heterogeneous proportional delays in this paper the problem of finite time stability analysis for a class of non autonomous neural networks with heterogeneous proportional delays is considered by introducing a novel constructive approach we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre specified finite time interval as a result we also obtain conditions for the power rate global stability of the system numerical examples are given to demonstrate the effectiveness and less restrictiveness of the results obtained in this paper

improved delay dependent stability criterion for neural networks with time varying delay in this paper the problem of delay dependent asymptotic stability criterion for neural networks with time varying delay has been considered a new class of lyapunov functional which contains a triple integral term is constructed to derive some new delay dependent stability criteria the obtained criteria are less conservative because free weighting matrices method and a convex optimization approach are considered finally numerical examples are given to illustrate the effectiveness of the proposed method

on backwards and forwards reachable sets bounding for perturbed time delay systems linear systems with interval time varying delay and unknown but bounded disturbances are considered in this paper we study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system firstly two definitions on forwards and backwards reachable sets where initial state vectors are not necessary to be equal to zero are introduced then by using the lyapunov krasovskii method two sufficient conditions for the existence of i the smallest possible outer bound of forwards reachable sets and ii the largest possible inter bound of backwards reachable sets are derived these conditions are presented in terms of linear matrix inequalities with two parameters need to tuned which therefore can be efficiently solved by combining existing convex optimization algorithms with a two dimensional search method to obtain optimal bounds lastly the obtained results are illustrated by four numerical examples

antithetic variates multivariate dependence and simulation of stochastic systems some theoretical and practical aspects antithetic and common random numbers for variance reduction in simulation of stochastic systems with dependent elements are considered a proof of their optimality in estimating the expected value of the response sum or the response difference of a pair of functions of vector arguments with dependent components is presented the efficiency of antithetic and common random numbers for variance reduction under different assumptions for the response functions is discussed applications to reliability networks and queueing systems are given

robust consensus control for a class of multi agent systems via distributed pid algorithm and weighted edge dynamics abstract this paper studies the robust proportional integral derivative pid consensus control for a class of linear multi agent systems mass with external disturbances different from the existing results both the consensus analysis and the transient performance characteristics for high order linear mass are considered based on a factorization of laplacian matrix the initial mas is firstly transformed into the so called weighted edge dynamics and then a design equivalence between the proposed pid consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results furthermore by combining lyapunov theory and barbalat s lemma it is proved that both the stabilization of weighted edge dynamics and the consensus of mas can be guaranteed even in the presence of external disturbances in particular some relationships between the transient time performance of weighted edge dynamics and the pid design parameters are given finally some numerical examples on lc oscillator network are provided to illustrate the validity of theoretical results