estimation of the domain of attraction for discrete time linear impulsive control systems with input saturation abstract this paper discusses the domain of attraction and stability analysis for discrete time linear impulsive systems with input saturation the first goal is to give a stable condition for the system the second is to present a strategy to find an inner estimate of the domain of attraction via establishing lyapunov functions and using other mathematical methods finally we present several examples to illustrate the validity of the conditions we have derived

stability and bifurcation for discrete time cohen grossberg neural network abstract this paper investigates a discrete time cohen grossberg neural network model some sufficient criteria ensuring the asymptotic stability of the equilibrium point for this model are derived moreover by choosing the appropriate bifurcation parameter we prove that neimark sacker bifurcation occurs when the bifurcation parameter exceeds a critical value we determine the direction and stability of bifurcation by applying the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical analysis are also given

pinning impulsive synchronization of reaction diffusion neural networks with time varying delays this paper investigates the exponential synchronization of reaction diffusion neural networks with time varying delays subject to dirichlet boundary conditions a novel type of pinning impulsive controllers is proposed to synchronize the reaction diffusion neural networks with time varying delays by applying the lyapunov functional method sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction diffusion neural networks with large and small delay sizes it is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network the technique used in this paper is also applicable to reaction diffusion networks with neumann boundary conditions numerical examples are presented to demonstrate the effectiveness of the theoretical results

impulsive stabilization and impulsive synchronization of discrete time delayed neural networks this paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete time delayed neural networks ddnns two types of ddnns with stabilizing impulses are studied by introducing the time varying lyapunov functional to capture the dynamical characteristics of discrete time impulsive delayed neural networks didnns and by using a convex combination technique new exponential stability criteria are derived in terms of linear matrix inequalities the stability criteria for didnns are independent of the size of time delay but rely on the lengths of impulsive intervals with the newly obtained stability results sufficient conditions on the existence of linear state feedback impulsive controllers are derived moreover a novel impulsive synchronization scheme for two identical ddnns is proposed the novel impulsive synchronization scheme allows synchronizing two identical ddnns with unknown delays simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of ddnns finally an application of the obtained impulsive synchronization result for two identical chaotic ddnns to a secure communication scheme is presented

bifurcations stability and monotonicity properties of a delayed neural network model abstract a delay differential equation modelling an artificial neural network with two neurons is investigated a linear stability analysis provides parameter values yielding asymptotic stability of the stationary solutions these can lose stability through either a pitchfork or a hopf bifurcation which is shown to be supercritical at appropriate parameter values an interaction takes place between the pitchfork and hopf bifurcations conditions are also given for the set of initial conditions that converge to a stable stationary solution to be open and dense in the functional phase space analytic results are illustrated with numerical simulations

globally asymptotical stability of discrete time analog neural networks some globally asymptotical stability criteria for the equilibrium states of a general class of discrete time dynamic neural networks with continuous states are presented using a diagonal lyapunov function approach the neural networks are assumed to have the asymmetrical weight matrices throughout the paper the resulting criteria are described by the diagonal stability of some matrices associated with the network parameters some novel stability conditions represented by either the existence of the positive diagonal solutions of the lyapunov equations or some inequalities are given using the equivalence between the diagonal stability and the schur stability for a nonnegative matrix some simplified global stability conditions are also presented finally some examples are provided for demonstrating the effectiveness of the global stability conditions presented

approximation on attraction domain of cohen grossberg neural networks abstract in this paper approximations of attraction domains of the asymptotically stable equilibrium points of some typical cohen grossberg neural networks are achieved most cohen grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain under some weak assumptions we are allowed to employ the optimal lyapunov method to obtain a lyapunov function for asymptotically stable equilibrium points of a given cohen grossberg neural network with the help of this lyapunov function we approximate the corresponding attraction domain by the iterative expansion approach numerical simulations also illustrate that the approximation obtained is really part of the attraction domain

multiple periodic solutions in impulsive hybrid neural networks with delays abstract the existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid hopfield type neural networks with both time dependent and distributed delays using the leray schauder fixed point theorem and lyapunov functionals the criteria given are easily verifiable possess many adjustable parameters and depend on impulses providing flexibility for the analysis and design of delayed neural networks with impulse effects examples are given

an uncertainty inequality for fourier dunkl series an uncertainty inequality for the fourier dunkl series introduced by the authors in o ciaurri j l varona a whittaker shannon kotel nikov sampling theorem related to the dunkl transform proc amer math soc 135 2007 2939 2947 is proved this result is an extension of the classical uncertainty inequality for the fourier series

the asymptotic shapes of periodic solutions of a singular delay differential system let f r r be given so that f 0 0 and f x 1 x ax2 bx3 o x3 as x 0 we characterize those small values of e 0 and r for which there are periodic solutions of periods approximately 2k with k n of the following system arising from a network of neurons formula the periodic solutions are synchronized if k is even and phase locked if k is odd we show that as e 0 these periodic solutions approach square waves if a 0 and b 0 or if a 0

uncertainty principles in harmonic analysis abstract let l 2 r n 2 1 generalizing the heisenberg uncertainty principle lower bounds for the variance of the measure x 2 dx are established under assumptions on the fourier transform tf if e is a subset of r n of codimension one which is suitably uniformly distributed and b is a parameter which measures the maximum distance from a point to e then the estimate var x 2 dx cb 2 holds provided e tf 2 d c b 1 for suitable constants c and c examples of sets e are families of parallel hyperspaces or concentric spheres analogous results are established for normalized l 2 functions on the sphere s n here the lower bound is inf y s n s n sin d x y 2 x 2 dx cb 2 and the hypothesis on the spherical harmonic expansion k 0 k is k a k 2 2 c b 1 where a is a set of integers with gaps at most b for both even and odd numbers

hopf bifurcation and stability of periodic solutions for van der pol equation with time delay abstract in this paper the van der pol equation with a time delay is considered where the time delay is regarded as a parameter it is found that hopf bifurcation occurs when this delay passes through a sequence of critical value a formula for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem

stability analysis of a delayed hopfield neural network in this paper we study a class of neural networks which includes bidirectional associative memory networks and cellular neural networks as its special cases by brouwer s fixed point theorem a continuation theorem based on gains and mawhin s coincidence degree matrix theory and inequality analysis we not only obtain some different sufficient conditions ensuring the existence uniqueness and global exponential stability of the equilibrium but also estimate the exponentially convergent rate our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity

on equilibria stability and instability of hopfield neural networks existence and uniqueness of equilibrium as well as its stability and instability of a continuous time hopfield neural network are studied a set of new and simple sufficient conditions are derived

global exponential stability of impulsive discrete time neural networks with time varying delays this paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete time neural networks with time varying delays firstly by means of the lyapunov stability theory some inequality analysis techniques and a discrete time halanay type inequality technique sufficient conditions for ensuring global exponential stability of discrete time neural networks are derived and the estimated exponential convergence rate is provided as well the obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete time neural networks with time varying delays finally numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria

delay induced periodicity in a neural netlet of excitation and inhibition abstract the dynamical behaviour of a two neuron netlet of excitation and inhibition with a transmission delay is investigated it is shown that in the absence of delay the netlet relaxes to the trivial resting state if the delay is of sufficient magnitude the network is excited to a temporally periodic cyclic behaviour the analytical mechanism for the onset of cyclic behaviour is through a hopf type bifurcation approximate solusions to the periodic output of the netlet is calculated stability of the temporally periodic cycle is investigated it is shown that the bifurcation is supercritical a related discrete version of the continuous time system is formulated it is found that the discrete system also displays a cyclic behaviour results of a number of computer simulations are displayed graphically the article concludes with a brief neurobiological discussion

convergence and periodicity in a discrete time network of two neurons with self connections abstract in this paper we study a class of difference systems modelling a two neuron network with feedback and mcculloch pitts type activation which includes the discrete version of the two neuron model with piecewise constant argument as its special case we obtain some interesting sufficient conditions insuring the convergence of solutions as well as the existence of periodic solutions

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

estimate of exponential convergence rate and exponential stability for neural networks estimates of exponential convergence rate and exponential stability are studied for a class of neural networks which includes hopfield neural networks and cellular neural networks both local and global exponential convergence are discussed theorems for estimation of the exponential convergence rate are established and the bounds on the rate of convergence are given the domains of attraction in the case of local exponential convergence are obtained simple conditions are presented for checking exponential stability of the neural networks

an uncertainty principle for ultraspherical expansions abstract motivated by heisenberg weyl type uncertainty principles for the torustand the spheres2due to breitenberger narowich ward and others we derive an uncertainty relation for radial functions on the spheressn r n 1and more generally for ultraspherical expansions on 0 in this setting the frequency variance of al2 function on 0 is defined by means of the ultraspherical differential operator which plays the role of a laplacian our proof is based on a certain first order differential difference operator on the doubled interval moreover using the densitiesftof gaussian measures on 0 with the timettending to 0 we show that the bound of our uncertainty principle is optimal

a family of operator splitting methods revisited abstract a family of operator splitting methods for maximal monotone operators is investigated it generalizes the douglas peaceman rachford varga class of methods in the way that it allows the scaling parameters to vary from iteration to iteration non monotonically conditions for convergence of methods within this family and for obtaining a linear rate of convergence are given these conditions cover more general cases than the existing ones

singular perturbation margin and generalised gain margin for linear time invariant systems in this paper we propose a singular perturbation margin spm and a generalised gain margin ggm as stability metrics for single input single output siso linear time invariant lti systems from the view of singular perturbations and regular perturbations which have bijective correspondences with the classical phase margin pm and the gain margin gm respectively both of the numerical and analytical time domain spm and ggm assessment methods are provided and relationships between the singular perturbation parameter pm of the perturbed system pm and spm of the nominal system and the monotonically increasing phase of the fast system are also revealed these results make it possible to assess the pm of the nominal system in the time domain for siso lti systems using the spm with a standardised testing system called pm gauge as demonstrated by examples the concepts of spm and ggm can be used as metrics of stability margins for linear time varying systems and nonlinear systems

solving convex programming problems with equality constraints by neural networks abstract this paper presents a neural network approach for solving convex programming problems with equality constraints after defining the energy function and neural dynamics of the proposed neural network we show the existence of an equilibrium point at which the neural dynamics becomes asymptotically stable it is shown that under proper conditions an optimal solution of the underlying convex programming problems is an equilibrium point of the neural dynamics and vise versa the configuration of the proposed neural network with an exact layout is provided for solving linear programming problems the operational characteristics of the neural network are demonstrated by numerical examples

relative error approximate versions of douglas rachford splitting and special cases of the admm we derive a new approximate version of the alternating direction method of multipliers admm which uses a relative error criterion the new version is somewhat restrictive and allows only one of the two subproblems to be minimized approximately but nevertheless covers commonly encountered special cases the derivation exploits the long established relationship between the admm and both the proximal point algorithm ppa and douglas rachford dr splitting for maximal monotone operators along with a relative error of the ppa due to solodov and svaiter in the course of analysis we also derive a version of dr splitting in which one operator may be evaluated approximately using a relative error criterion we computationally evaluate our method on several classes of test problems and find that it significantly outperforms several alternatives on one problem class

paper maximal lyapunov functions and domains of attraction for autonomous nonlinear systems in this paper we present various theoretical and computational methods for estimating the domain of attraction of an autonomous nonlinear system these methods are based on the concept of a maximal lyapunov function which is introduced in this paper a partial differential equation characterizing a maximal lyapunov function is derived and the relationships of this equation as compared to zubov s partial differential equation are discussed an iterative procedure is given for solving the new partial differential equation this procedure yields lyapunov function candidates that are rational functions rather than polynomials the method is applied to four two dimensional examples and one three dimensional example and it is shown that the estimates obtained using this method are in many cases substantially better than those obtained using known methods

configurations of steady states for hopfield type neural networks the dependence of the steady states on the external input vector i for the continuous time and discrete time hopfield type neural networks of n neurons is discussed conditions for the existence of one or several paths of steady states are derived it is shown that in some conditions for an external input i there may exist at least 2 n exponentially stable steady states called configuration of steady states and their regions of attraction are estimated this means that there exist 2 n paths of exponentially stable steady states defined on a certain set of input values conditions assuring the transfer of a configuration of exponentially stable steady states to another configuration of exponentially stable steady states by successive changes of the external input are obtained these results may be important for the design and maneuvering of hopfield type neural networks used to analyze associative memories

periodic solutions for a two neuron network with delays in this paper we use the coincidence degree theory to establish new results on the existence of w periodic solutions for a two neuron network model

control procedures using domains of attraction abstract a technique of gradual approximation of the domain of attraction in the case of nonlinear continuous and discrete analytical dynamical systems is presented the technique is based on the gradual extension of the embryo of the optimal lyapunov function and gives at each step a new open and non empty piece of the domain of attraction for a nonlinear dynamical system with control defined by an analytical autonomous system of differential equations or difference equations using domains of attraction it is shown that two steady states which belong to an analytic path of asymptotically stable steady states can be transferred gradually one in the other by successive changes of the values of the control parameters numerical examples are given for the alflex reentry vehicle and for a discrete dynamical system considered recently in the literature

stability bifurcation and multistability in a system of two coupled neurons with multiple time delays a system of delay differential equations representing a model for a pair of neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself is studied conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements it is shown that the trivial fixed point may lose stability via a pitchfork bifurcation a hopf bifurcation or one of three types of codimension two bifurcations multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations

methods for determination and approximation of the domain of attraction abstract in this paper an r analytical function and the sequence of its taylor polynomials which are lyapunov functions different from those of vanelli and vidyasagar automatica 21 1 1985 69 80 is presented in order to determine and approximate the domain of attraction of the exponentially asymptotically stable zero steady state of an autonomous r analytical system of differential equations the analytical function and the sequence of its taylor polynomials are constructed by recurrence formulae using the coefficients of the power series expansion of f at 0

stability and bifurcation analysis on a discrete time neural network using techniques developed by kuznetsov to discrete time systems we study the stability of the equilibrium 0 0 and neimark sacker bifurcation also called hopf bifurcation for map of a discrete time neural network system the obtained results are less restrictive and improve upon the existing ones on neimark sacker bifurcation of discrete time neural network with special classes of transfer functions the theoretical analyses are verified by numerical simulations our results have potential applications in neural networks

oscillation susceptibility analysis along the path of longitudinal flight equilibriums abstract in this paper the oscillation susceptibility of an aircraft in a longitudinal flight with constant forward velocity is analyzed in different flight models conditions which ensure such a flight and equations governing the flight are presented the stability of the equilibriums appearing is analyzed and the existence of hopf bifurcations and saddle node bifurcations is researched for two aircrafts in a simplified model it is shown that saddle node bifurcations are present and there are no hopf bifurcations it is shown that for the elevator deflection there are two turning points e e having the property that if e e e then the angle of attack and the pitch rate q oscillate with the same period while the pitch angle increases decreases tending to the behavior of the aircraft is simulated in the simplified model when the elevator deflection e varies in the range e e and when e leaves this range for one of the aircrafts the analysis is performed also in the not simplified model showing the differences between the results obtained in different models

on a planar system modelling a neuron network with memory abstract we consider a delay differential equation modelling a network of two neurons with memory the situations without self connections and two delays and with self connections and two equal delays are addressed in terms of local stability and bifurcation analysis in the first case the dynamical behavior is studied by taking one of the delays as the bifurcating parameter namely the hopf bifurcation whose existence was proven in former works occurs as the delay crosses some critical values and is completely described conditions ensuring the stability of the periodic cycles are given when self connections are present hopf and pitchfork bifurcations co exist and the equation describing the flow on the center manifold is derived

exponential stability of discrete time hopfield neural networks in this paper some sufficient conditions for the local and global exponential stability of the discrete time hopfield neural networks with general activation functions are derived which gen eralize those existing results by means of m matrix theory and some inequality analysis techniques the exponential convergence rate of the neural networks to the equilibrium is estimated and for the local exponential stability the basin of attraction of the stable equilibrium is also characterized 2004 elsevier ltd all rights reserved

differential difference operators associated to reflection groups there is a theory of spherical harmonics for measures invariant under a finite reflection group the measures are products of powers of linear functions whose zero sets are the mirrors of the reflections in the group times the rotation invariant measure on the unit sphere in rn a commutative set of differential difference operators each homogeneous of degree 1 is the analogue of the set of first order partial derivatives in the ordinary theory of spherical harmonics in the case of r2 and dihedral groups there are analogues of the cauchy riemann equations which apply to gegenbauer and jacobi polynomial expansions the analysis of orthogonality structures for polynomials in several variables is a problem of vast dimensions this paper is part of an ongoing program to establish a workable theory for one particular class the underlying structure is based on finite coxeter groups these are finite groups acting on euclidean space generated by reflections in the zero sets of a collection of linear functions the roots the weight functions for the orthogonality are products of powers of these linear functions restricted to the surface of the unit sphere in addition the weight function is required to be invariant under the action of the group the resulting theory has strong similarities to the theory of spherical harmonics this was established in previous papers of the author 3 4 5 most notably a homogeneous polynomial is orthogonal to all polynomials of lower degree if and only if it is annihilated by a certain second order differential difference operator ordinary partial differentiation acts as an endomorphism on ordinary harmonic functions the use of such operators and their adjoints leads to recurrence formulas and orthogonal decompositions for harmonic polynomials in this paper we construct a commutative set of first order differentialdifference operators associated to the second order operator previously mentioned received by the editors june 1 1987 1980 mathematics subject classification 1985 revision primary 33a45 33a65 20h15 secondary 20c30 42c10 51f15

stability analysis of discrete time recurrent neural networks with stochastic delay this paper is concerned with the stability analysis of discrete time recurrent neural networks rnns with time delays as random variables drawn from some probability distribution by introducing the variation probability of the time delay a common delayed discrete time rnn system is transformed into one with stochastic parameters improved conditions for the mean square stability of these systems are obtained by employing new lyapunov functions and novel techniques are used to achieve delay dependence the merit of the proposed conditions lies in its reduced conservatism which is made possible by considering not only the range of the time delays but also the variation probability distribution a numerical example is provided to show the advantages of the proposed conditions

a new approach for estimating the attraction domain for hopfield type neural networks in this letter using methods proposed by e kaslik st balint and their colleagues we develop a new method expansion approach for estimating the attraction domain of asymptotically stable equilibrium points of hopfield type neural networks we prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient the numerical results that obtained in the application examples including the network system considered by e kaslik l br escu and st balint indicate that the proposed approach is able to achieve better attraction domain estimation

a note on stability of analog neural networks with time delays this note presents a generalized sufficient condition which guarantees stability of analog neural networks with time delays the condition is derived using a lyapunov functional and the stability criterion is stated as the equilibrium of analog neural networks with delays is globally asymptotically stable if the product of the norm of connection matrix and the maximum neuronal gain is less than one

global attractivity of a synchronized periodic orbit in a delayed network abstract we consider an artificial neural network where the signal transmission is of a digital mcculloch pitts nature and is delayed due to the finite switching speed of neurons amplifiers for a particular connection topology we show that all solutions starting from nonoscillatory initial states will be eventually synchronized and stabilized at a unique limit cycle and hence such a network can be used as a synchronized oscillator

uncertainty principles for jacobi expansions abstract in this paper an uncertainty principle for jacobi expansions is derived as a generalization of that for ultraspherical expansions by rosler and voit indeed a stronger inequality is proved which is new even for fourier cosine or ultraspherical expansions a complex base of exponential type on the torus z c z 1 related to jacobi polynomials is introduced which are the eigenfunctions both of certain differential difference operators of the first order and the second order an uncertainty principle related to such exponential base is also proved

monotone operator theory in convex optimization several aspects of the interplay between monotone operator theory and convex optimization are presented the crucial role played by monotone operators in the analysis and the numerical solution of convex minimization problems is emphasized we review the properties of subdifferentials as maximally monotone operators and in tandem investigate those of proximity operators as resolvents in particular we study new transformations which map proximity operators to proximity operators and establish connections with self dual classes of firmly nonexpansive operators in addition new insights and developments are proposed on the algorithmic front

existence and stability of equilibria of the continuous time hopfield neural network the qualitative properties of the continuous time hopfield neural network are investigated by using the cauchy existence theorem of ordinary differential equations a set of new and simple sufficient conditions guaranteeing the existence and uniqueness of equilibrium is derived furthermore global and asymptotical stability conditions are established by means of lyapunov method

global exponential stability of impulsive delay difference equation abstract in this paper an impulsive delay difference equation is considered by establishing an impulsive delay difference inequality and using the properties of cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of the impulsive delay difference equation are obtained the results extend and improve the earlier publications an example is given to demonstrate the effectiveness of the theory

a note on the paper by eckstein and svaiter on general projective splitting methods for sums of maximal monotone operators in their recent paper from 2009 siam j control optim 48 2009 pp 787 811 j eckstein and b f svaiter proposed a very general and flexible splitting framework for finding a zero of the sum of finitely many maximal monotone operators in this short note we provide a technical result that allows for the removal of eckstein and svaiter s assumption that the sum of the operators be maximal monotone or that the underlying hilbert space be finite dimensional

a family of projective splitting methods for the sum of two maximal monotone operators a splitting method for two monotone operators a and b is an algorithm that attempts to converge to a zero of the sum a b by solving a sequence of subproblems each of which involves only the operator a or only the operator b prior algorithms of this type can all in essence be categorized into three main classes the douglas peaceman rachford class the forward backward class and the little used double backward class through a certain extended solution set in a product space we construct a fundamentally new class of splitting methods for pairs of general maximal monotone operators in hilbert space our algorithms are essentially standard projection methods using splitting decomposition to construct separators we prove convergence through fejer monotonicity techniques but showing fejer convergence of a different sequence to a different set than in earlier splitting methods our projective algorithms converge under more general conditions than prior splitting methods allowing the proximal parameter to vary from iteration to iteration and even from operator to operator while retaining convergence for essentially arbitrary pairs of operators the new projective splitting class also contains noteworthy preexisting methods either as conventional special cases or excluded boundary cases

hopf bifurcating periodic orbits in a ring of neurons with delays in this paper we consider a ring of neurons with self feedback and delays the linear stability of the model is investigated by analyzing the associated characteristic transcendental equation based on the normal form approach and the center manifold theory we derive the formula for determining the properties of hopf bifurcating slowly oscillating periodic orbits for a ring of neurons with delays including the direction of hopf bifurcation stability of the hopf bifurcating slowly oscillating periodic orbits and so on moreover by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups we not only investigate the effect of synaptic delay of signal transmission on the pattern formation but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio temporal patterns

stable periodic orbits in nonlinear discrete time neural networks with delayed feedback we consider a nonlinear discrete time system x n 1 x n g y n k y n 1 y n g x n k n n arising as a discrete time network of two neurons with mcculloch pitts nonlinearity where 0 1 k is a positive integer and g is a signal transmission function with a threshold we obtain a stable 4 k 1 periodic orbit in some regions of the parameters and we describe asymptotic behaviors of the system in other regions of

improved global exponential stability for delay difference equations with impulses abstract in this paper by means of constructing an impulsive delay difference inequality we study the global exponential stability for a class of delay difference equations with impulses a new criterion ensuring the global exponential stability of the equilibrium point is obtained which is less restrictive and conservative than that given in the earlier reference an illustrative example is given to demonstrate the effectiveness and advantage of the obtained result