existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time varying coefficients and mixed delays this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to recurrent delayed neural networks several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain furthermore several methods are applied to establish sufficient criteria for the globally exponential stability of this system the approaches are based on constructing suitable lyapunov functionals and the well known banach contraction mapping principle moreover the attractivity and exponential stability of the pseudo almost periodic solution are also considered for the system a numerical example is given to illustrate the effectiveness of our results

technical communique comments on finite time stability of time delay systems recently proposed conditions on finite time stability in time delay systems are revisited and it is shown that they are incorrect general comments on possibility of finite time convergence in time delay systems and a necessary condition are given

finite time stability and stabilization of time delay systems finite time stability and stabilization of retarded type functional differential equations are developed first a theoretical result on finite time stability inspired by the theory of differential equations using lyapunov functionals is given as it may appear not easily usable in practice we show how to obtain finite time stabilization of linear systems with delays in the input by using an extension of artstein s model reduction to nonlinear feedback with this approach we give an explicit finite time controller for scalar linear systems and for the chain of integrators with delays in the input

riesz transforms associated with the number operator on the walsh system and the fermions abstract we prove that for 2 p f l p 1 1 n 1 2 f p is equivalent to n j 1 f f e j 2 1 2 p where is the discrete laplacian and the constants do not depend on f nor n such an equivalence is false for 1 p 1 2 f p similar results are obtained for fermions t viewed as some 2 n 2 n matrices equipped with their schatten norm c p comparing n 1 2 t p with n j 1 d j t 2 s 1 2 p where the d j s are the annihi lation operators on the fermions and n n j 1 d j d j is the number operator

finite time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller this paper is concerned about the finite time stabilizability and instabilizability for a class of delayed memristive neural networks dmnns through the design of a new nonlinear controller algebraic criteria based on m matrix are established for the finite time stabilizability of dmnns and the upper bound of the settling time for stabilization is estimated in addition finite time instabilizability algebraic criteria are also established by choosing different parameters of the same nonlinear controller the effectiveness and the superiority of the obtained results are supported by numerical simulations

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

an improved algebraic criterion for global exponential stability of recurrent neural networks with time varying delays this brief paper presents an m matrix based algebraic criterion for the global exponential stability of a class of recurrent neural networks with decreasing time varying delays the criterion improves some previous criteria based on m matrix and is easy to be verified with the connection weights of the recurrent neural networks with decreasing time varying delays in addition the rate of exponential convergence can be estimated via a simple computation based on the criterion herein

robust stability and stabilization of fractional order interval systems with the fractional order alpha the 0 alpha 1 case this technical note firstly presents a sufficient and necessary condition for the robust asymptotical stability of fractional order interval systems with the fractional order satisfying 0 1 and then a sufficient condition for the robust asymptotical stabilization of such fractional order interval systems is derived all the results are obtained in terms of linear matrix inequalities finally two illustrative examples are given to show that our results are effective for checking the robust stability and designing the robust stabilizing controller for fractional order interval systems

delay independent robust stability analysis of delayed fractional quaternion valued leaky integrator echo state neural networks with quad condition abstract this paper studies the stability of fractional order fo continuous time quaternion valued leaky integrator echo state neural networks nn the delay independent robust stability of nn with quad vector field activation functions under time varying delays is derived the analysis follows the fo lyapunov theorem while decomposing the nn into four real valued systems the existence and uniqueness of the equilibrium point are also verified by means of a contraction map on the decomposed nn the new approach is tested in the stability analysis of the fo quaternion valued echo state nn whitout time delays complex valued echo state and quaternion complex valued hopfield nn with without time delays two numerical examples demonstrate the feasibility of the proposed method

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

sharp lp estimates for discrete second order riesz transforms we show that multipliers of second order riesz transforms on products of discrete abelian groups enjoy the lp estimate p 1 where p max p q and p and q are conjugate exponents this estimate is sharp if one considers all multipliers of the form i iriri with i 1 and infinite groups in the real valued case we obtain better sharp estimates for some specific multipliers such as i iriri with 0 i 1 these are the first known precise lp estimates for discrete calderon zygmund operators

dimension free estimates for discrete riesz transforms on products of abelian groups let g be a lca group with a fixed g0 g spanning an infinite subgroup let j acting on l2 gn be translation by go in the jth coordinate the discrete derivatives j i j define a discrete laplacian l j 1n j j and discrete riesz transforms rj jl 12 we get dimension free estimates cp f lp gn j 1n rj f 2 rj f 212lp gn cp f lp gn for 2 p the right side inequality is false for 1 p 2 but we give the substitute we also consider the case where gpg0 is a cyclic group

about riesz transforms on the heisenberg groups see also m1 subsequently several other proofs have been given of probabilistic b ba see also g v or analytic d r p nature also p a meyer has given in m2 a similar result in the gaussian setting the aim of this work is to prove analogous inequalities for the family of heisenberg groups h n instead of the family of euclidean spaces r n the euclidean proofs do not adapt to the non commutative situation of h however our method is reminiscent of some ideas of the proofs by duoandikoetxearubio de francia d r and pisier p a new feature is however the central r6te played by the heat kernel and our proof heavily relies on its explicit expression in h n given by gavean g and hulanicki h let us recall finally that apart from any question of uniformity the boundedness of the riesz transforms on every nilpotent lie group is a well known issue see l v

rate of convergence of basic neural network operators to the unit univariate case this chapter deals with the determination of the rate of convergence to the unit of some neural network operators namely the normalized bell and squashing type operators

new algebraic criteria for synchronization stability of chaotic memristive neural networks with time varying delays in this brief we consider the exponential synchronization of chaotic memristive neural networks with time varying delays using the lyapunov functional method and inequality technique the dynamic analysis here employs the theory of differential equations with discontinuous right hand side as introduced by filippov the designing laws in the synchronization of neural networks are proposed via state or output coupling in addition the new proposed algebraic criteria are very easy to verify and they also enrich and improve the earlier publications finally an example is given to show the effectiveness of the obtained results

synchronization of fractional order linear complex networks with directed coupling topology abstract the synchronization of fractional order complex networks with general linear dynamics under directed connected topology is investigated the synchronization problem is converted to an equivalent simultaneous stability problem of corresponding independent subsystems by use of a pseudo state transformation technique and real jordan canonical form of matrix sufficient conditions in terms of linear matrix inequalities for synchronization are established according to stability theory of fractional order differential equations in a certain range of fractional order the effects of the fractional order on synchronization is clearly revealed conclusions obtained in this paper generalize the existing results three numerical examples are provided to illustrate the validity of proposed conclusions

stability and pinning synchronization analysis of fractional order delayed cohen grossberg neural networks with discontinuous activations abstract this article we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed cohen grossberg neural networks with discontinuous neuron activation functions fcgnndds first under the framework of filippov theory and differential inclusion theoretical analysis the global existence of filippov solution for fcgnndds is studied by means of the given growth condition second by virtue of suitable lyapunov functional young inequality and comparison theorem for fractional order delayed linear system some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations third the global asymptotic synchronization condition for fcgnndds is obtained based on the pinning control at last two numerical simulations are given to verify the theoretical findings

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the paper presents theoretical results on the global exponential periodicity and stability of a class of memristor based recurrent neural networks with multiple delays the dynamic analysis in the paper employs the theory of differential equations with discontinuous right hand side as introduced by filippov by using the inequality techniques and a useful lyapunov functional some new testable algebraic criteria are obtained for ensuring the existence and global exponential stability of periodic solution of the system the model based on the memristor widens the application scope for the design of neural networks and the new effective results also enrich the toolbox for the qualitative analysis of neural networks

mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic hopfield neural networks abstract recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention but there has been little work on the stability analysis of the numerical solutions to delayed stochastic hopfield neural networks dshnns so far the aim in this paper is to study the mean square exponential stability of the split step theta sst method and the stochastic linear theta slt method for the underlying model it is proved that for any 0 1 2 there exists a constant 0 depending on such that the numerical schemes produced by the sst method and the slt method are mean square exponentially stable for 0 under the same assumptions as those to guarantee the mean square exponential stability of the underlying continuous model for the case 1 2 1 we show the same stability conclusion for all 0 to carry out the required conclusion a novel technique for the stability analysis of discrete numerical schemes with multi time delays namely the weighted sum lyapunov functional method is proposed finally a numerical example is given to illustrate the application of the suggested methods and to verify the stability conclusions obtained

bellman function and linear dimension free estimates in a theorem of bakry by using an explicit bellman function we prove a bilinear embedding theorem for the laplacian associated with a weighted riemannian manifold m having the bakry emery curvature bounded from below the embedding acting on the cartesian product of lp m and lq t m 1 p 1 q 1 involves estimates which are independent of the dimension of the manifold and linear in p as a consequence we obtain linear dimension free estimates of the lp norms of the corresponding shifted riesz transform all our proofs are analytic

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

new criteria for global robust stability of delayed neural networks with norm bounded uncertainties in this paper we study the global asymptotic robust stability of delayed neural networks with norm bounded uncertainties by employing the lyapunov stability theory and homeomorphic mapping theorem we derive some new types of sufficient conditions ensuring the existence uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope bounded activation functions an important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties of symmetric matrices associated with the uncertainty sets of the network parameters the obtained results are shown to be generalizations of some of the previously published corresponding results some comparative numerical examples are also constructed to compare our results with some closely related existing literature results

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

monostability and multistability for almost periodic solutions of fractional order neural networks with unsaturating piecewise linear activation functions since the unsaturating activation function is unbounded more complex dynamics may exist in neural networks with this kind of activation function in this article monostability and multistability results of almost periodic solutions are developed for fractional order neural networks with unsaturating piecewise linear activation functions some globally mittag leffler attractive sets are given and the existence of globally mittag leffler stable almost periodic solution is demonstrated by using ascoli arzela theorem in particular some sufficient conditions are provided to ascertain the multistability of almost periodic solutions based on locally positively invariant set it shows that there exists an almost periodic solution in each positively invariant set and all trajectories converge to this periodic trajectory in that rectangular area two illustrative examples are provided to demonstrate the effectiveness of the proposed sufficient criteria

a sharp inequality for martingale transforms and the unconditional basis constant of a monotone basis in 0 1 let 1 1 k 1 p k 1 p satisfies cp p log 2 j p where y e 2 and a2 i log y 2 2 log y 2 y 2 the best constant 2 2 2 1 y equals the unconditional basis constant of a monotone basis of lp 0 1

undamped oscillations generated by hopf bifurcations in fractional order recurrent neural networks with caputo derivative in this paper a fractional order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated such as the stability hopf bifurcations and undamped oscillations the stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate order neural network based on the stability analysis the critical values of the fractional order are identified where hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state then the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate order networks meanwhile it is shown that the incommensurate order neural network can also exhibit a hopf bifurcation as the network parameter passes through a critical value which can be determined exactly the frequency and amplitude of bifurcated oscillations are determined

on singular integral and martingale transforms linear equivalences of norms of vector valued singular integral operators and vector valued martingale transforms are studied in particular it is shown that the umd constant of a banach space x equals the norm of the real or the imaginary part of the beurling ahlfors singular integral operator acting on l p x r 2 with p 1 moreover replacing equality by a linear equivalence this is found to be a typical property of even multipliers a corresponding result for odd multipliers and the hilbert transform is given as a corollary we obtain that the norm of the real part of the beurling ahlfors operator equals p 1 with p max p p p 1 where the novelty is the lower bound

schur complements and statistics abstract in this paper we discuss various properties of matrices of the type s h ge 1 f which we call the schur complement of e in a e f g h the matrix e is assumed to be nonsingular when e is singular or rectangular we consider the generalized schur complements s h ge f where e is a generalized inverse of e a comprehensive account of results pertaining to the determinant the rank the inverse and generalized inverses of partitioned matrices and the inertia of a matrix is given both for schur complements and for generalized schur complements we survey the known results in a historical perspective and obtain several extensions numerous applications in numerical analysis and statistics are included the paper ends with an exhaustive bibliography of books and articles related to schur complements

robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects this paper focuses on the hybrid effects of parameter uncertainty stochastic perturbation and impulses on global stability of delayed neural networks by using the ito formula lyapunov function and halanay inequality we established several mean square stability criteria from which we can estimate the feasible bounds of impulses provided that parameter uncertainty and stochastic perturbations are well constrained moreover the present method can also be applied to general differential systems with stochastic perturbation and impulses

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

existence and uniform stability analysis of fractional order complex valued neural networks with time delays this paper deals with the problem of existence and uniform stability analysis of fractional order complex valued neural networks with constant time delays complex valued recurrent neural networks is an extension of real valued recurrent neural networks that includes complex valued states connection weights or activation functions this paper explains sufficient condition for the existence and uniform stability analysis of such networks three numerical simulations are delineated to substantiate the effectiveness of the theoretical results

finite time stability and stabilization of a class of nonlinear time delay systems this paper investigates the finite time stability fts and stabilization for a class of nonlinear time delay systems and proposes some new results first an equivalent form is presented for the systems by a coordinate transformation and a criterion on the fts is obtained for nonlinear time delay systems via the razumikhin approach r approach then based on the criterion and the equivalent form some delay independent and delay dependent conditions on the fts are derived for this class of systems by constructing a new lyapunov function third we use the obtained fts results to investigate the finite time stabilization problem and present a control design procedure for the time delay systems it is shown that our method can avoid solving nonlinear matrix inequalities by transferring them into the form of linear matrix inequalities which can be easily solved with the lmi toolbox of matlab finally study of illustrative examples shows that the results obtained in this paper work very well in the ft

generalized halanay inequalities and their applications to neural networks with unbounded time varying delays in this brief we discuss some variants of generalized halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks integro differential systems and volterra functional differential equations we provide some generalizations of the halanay inequality which is more accurate than the existing results as applications we discuss invariant set dissipative synchronization and global asymptotic stability for the hopfield neural networks with infinite delays we also prove that the dynamical systems with unbounded time varying delays are globally asymptotically stable

novel stability analysis for recurrent neural networks with multiple delays via line integral type l k functional this paper studies the stability problem of a class of recurrent neural networks rnns with multiple delays by using an augmented matrix vector transformation for delays and a novel line integral type lyapunov krasovskii functional a less conservative delay dependent global asymptotical stability criterion is first proposed for rnns with multiple delays the obtained stability result is easy to check and improve upon the existing ones then two numerical examples are given to verify the effectiveness of the proposed criterion

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

functional calculus for generators of symmetric contraction semigroups we prove that every generator of a symmetric contraction semigroup on a finite measure space admits for 1 p a hormander type holomorphic functional calculus on lp in the sector of angle p arcsin 1 2 p the obtained angle is optimal

distance matrices and regular figures abstract a regular figure which includes all regular polygons is a set of points on a hypersphere whose center coincides with their centroid we characterize all regular figures as those whose points generate a euclidean distance matrix edm with eigenvector e the vector of all ones restricting the classical maps of schoenberg gower and critchley for all edms to the subcone of edms with eigenvector e yields new geometrical information about the generating points and a simple formula for the radius of the hypersphere

bellman functions and dimension free lp estimates for the riesz transforms in bessel settings abstract in this article we prove dimension free l p boundedness of riesz transforms associated with a bessel differential operator we obtain explicit estimates of the l p norms for the bessel riesz transforms in terms of p establishing a linear behavior with respect to p we use the bellman function technique to prove a bilinear dimension free inequality involving poisson semigroups defined through this bessel operator

a one layer recurrent neural network with a discontinuous hard limiting activation function for quadratic programming in this paper a one layer recurrent neural network with a discontinuous hard limiting activation function is proposed for quadratic programming this neural network is capable of solving a large class of quadratic programming problems the state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints in addition a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming simulation results on numerical examples and support vector machine svm learning show the effectiveness and performance of the neural network

passivity and passification of memristor based recurrent neural networks with additive time varying delays this paper presents a new design scheme for the passivity and passification of a class of memristor based recurrent neural networks mrnns with additive time varying delays the predictable assumptions on the boundedness and lipschitz continuity of activation functions are formulated the systems considered here are based on a different time delay model suggested recently which includes additive time varying delay components in the state the connection between the time varying delay and its upper bound is considered when estimating the upper bound of the derivative of lyapunov functional it is recognized that the passivity condition can be expressed in a linear matrix inequality lmi format and by using characteristic function method for state feedback passification it is verified that it is apathetic to use immediate or delayed state feedback by constructing a lyapunov krasovskii functional and employing jensen s inequality and reciprocal convex combination technique together with a tighter estimation of the upper bound of the cross product terms derived from the derivatives of the lyapunov functional less conventional delay dependent passivity criteria are established in terms of lmis moreover second order reciprocally convex approach is employed for deriving the upper bound for terms with inverses of squared convex parameters the model based on the memristor with additive time varying delays widens the application scope for the design of neural networks finally pertinent examples are given to show the advantages of the derived passivity criteria and the significant improvement of the theoretical approaches

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

robust finite time stabilization of fractional order neural networks with discontinuous and continuous activation functions under uncertainty this paper is concerned with robust finite time stabilization for a class of fractional order neural networks fnns with two types of activation functions i e discontinuous and continuous activation function under uncertainty it is worth noting that there exist few results about fnns with discontinuous activation functions which is mainly because classical solutions and theories of differential equations cannot be applied in this case especially there is no relevant finite time stabilization research for such system and this paper makes up for the gap the existence of global solution under the framework of filippov for such system is guaranteed by limiting discontinuous activation functions according to set valued analysis and kakutani s fixed point theorem we obtain the existence of equilibrium point in particular based on differential inclusion theory and fractional lyapunov stability theory several new sufficient conditions are given to ensure finite time stabilization via a novel discontinuous controller and the upper bound of the settling time for stabilization is estimated in addition we analyze the finite time stabilization of fnns with lipschitz continuous activation functions under uncertainty the results of this paper improve corresponding ones of integer order neural networks with discontinuous and continuous activation functions finally three numerical examples are given to show the effectiveness of the theoretical results

global exponential stability and global convergence in finite time of delayed neural networks with infinite gain this paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections and neuron activations belonging to the set of discontinuous monotone increasing and possibly unbounded functions the discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity while the delay accounts for the finite switching speed of the neuron amplifiers or the finite signal propagation speed it is known that the delay in combination with high gain nonlinearities is a particularly harmful source of potential instability the goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay more precisely conditions are given under which there is a unique equilibrium point of the neural network which is globally exponentially stable for the states with a known convergence rate the conditions are easily testable and independent of the delay moreover global convergence in finite time of the state and output is investigated in doing so new interesting dynamical phenomena are highlighted with respect to the case without delay which make the study of convergence in finite time significantly more difficult the obtained results extend previous work on global stability of delayed neural networks with lipschitz continuous neuron activations and neural networks with discontinuous neuron activations but without delays

brief paper markovian jump delayed hopfield networks with multiplicative noise a non symmetric version of hopfield networks subject to state multiplicative noise pure time delay and markov jumps is considered such networks arise in the context of visuo motor control loops and may therefore be used to mimic their complex behavior in this paper we adopt the lur e postnikov systems approach to analyze the stochastic stability and the l 2 gain of generalized hopfield networks including these effects

on the ell p norm of the discrete hilbert transform using a representation of the discrete hilbert transform in terms of martingales arising from doob h processes we prove that its lp norm 1 p is bounded above by the lp norm of the continuous hilbert transform together with the already known lower bound this resolves the long standing conjecture that the norms of these operators are equal

exponential stabilization of neural networks with various activation functions and mixed time varying delays this paper presents some results on the global exponential stabilization for neural networks with various activation functions and time varying continuously distributed delays based on augmented time varying lyapunov krasovskii functionals new delay dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities a numerical example is given to illustrate the feasibility of our results

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

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

finite time global stabilization by means of time varying distributed delay feedback the paper contains certain results concerning the finite time global stabilization for triangular control systems described by retarded functional differential equations by means of time varying distributed delay feedback these results enable us to present solutions to feedback stabilization problems for systems with delayed input the results are obtained by using the backstepping technique

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

eigenstructure of distance matrices with an equal distance subset abstract we characterize the distance matrices with an equal distance subset in terms of eigenstructure and determine edms in this class by examination of a lower dimensional matrix

exponential stabilization of memristive neural networks with time delays in this paper a general class of memristive neural networks with time delays is formulated and studied some sufficient conditions in terms of linear matrix inequalities are obtained in order to achieve exponential stabilization the result can be applied to the closed loop control of memristive systems in particular several succinct criteria are given to ascertain the exponential stabilization of memristive cellular neural networks in addition a simplified and effective algorithm is considered for design of the optimal controller these conditions are the improvement and extension of the existing results in the literature two numerical examples are given to illustrate the theoretical results via computer simulations

chaotic behavior in noninteger order cellular neural networks in this paper a simple system showing chaotic behavior is introduced it is based on the well known concept of cellular neural networks cnns which have already given good results in generating complex dynamics the peculiarity of the cnn model consists in the fact that it replaces the traditional first order cell with a noninteger order one the introduction of the fractional cell with a suitable choice of the coupling parameters leads to the onset of chaos in a simple two cell system a theoretical approach based on the harmonic balance theory has been used to investigate the existence of chaos a circuit realization of the proposed fractional two cell chaotic cnn is reported and the corresponding strange attractor is also shown

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

approximation by matrices positive semidefinite on a subspace abstract we obtain the best approximation to a matrix by matrices positive semidefinite on a subspace as a by product we present two new characterizations of euclidean distance matrices

finite time stabilization of fractional order uncertain chain of integrator an integral sliding mode approach in this technical note a novel methodology for robust finite time stabilization of a chain of uncertain fractional order integrator is proposed this is achieved by first designing a nominal controller which stabilizes the system in finite time an integral sliding mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding mode control is the negative of the disturbance and hence the disturbance is cancelled an improved strategy with more general kind of uncertainty is also proposed numerical examples are presented to illustrate the proposed methods

the approximation operators with sigmoidal functions the aim of this paper is to investigate the error which results from the method of approximation operators with logarithmic sigmoidal function by means of the method of extending functions a class of feed forward neural network operators is introduced using these operators as approximation tools the upper bounds of errors in uniform norm approximating continuous functions are estimated also a class of quasi interpolation operators with logarithmic sigmoidal function is constructed for approximating continuous functions defined on the total real axis

new criteria on finite time stability of fractional order hopfield neural networks with time delays in this article the finite time stability fts of fractional order hopfield neural networks with time delays fhnntds is studied a widely used inequality in investigating the stability of the fractional order neural networks is fractional order gronwall inequality related to the mittag leffler function which cannot be directly used to study the stability of the factional order neural networks with time delays in the existing works related to fractional order gronwall inequality with time delays the order 0 was divided into two cases 0 0 5 and 0 5 in this article a new fractional order gronwall integral inequality with time delay and the unified form for all the fractional order 0 is developed which can be widely applied to investigate fts of various fractional order systems with time delays based on this new inequality a new criterion for the fts of fhnntds is derived compared with the existing criteria in which fractional order 0 1 was divided into two cases 0 0 5 and 0 5 1 the obtained results in this article are presented in the unified form of fractional order 0 1 and convenient to verify more importantly the criteria in this article are less conservative than some existing ones finally two numerical examples are given to demonstrate the validity of the proposed results

finite time stabilization of delayed memristive neural networks discontinuous state feedback and adaptive control approach in this paper a general class of delayed memristive neural networks dmnns system described by functional differential equation with discontinuous right hand side is considered under the extended filippov framework we investigate the finite time stabilization problem for dmnns by using the famous finite time stability theorem and the generalized lyapunov functional method to do so we design two classes of novel controllers including discontinuous state feedback controller and discontinuous adaptive controller without assuming the boundedness and monotonicity of the activation functions several sufficient conditions are given to stabilize the states of this class of dmnns in finite time moreover the upper bounds of the settling time for stabilization are estimated finally numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results

finite time stabilization of nonlinear systems with parametric and dynamic uncertainties in this note non smooth finite time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated to solve this problem the input to state stability property is used to characterize unmeasured dynamic uncertainties a constructive partial state control design is proposed on the basis of involved combined use of lyapunov backstepping and input to state stability techniques under small gain type local conditions a solution for the finite time regulation of a class of uncertain nonlinear systems is obtained

multivariate hyperbolic tangent neural network approximation here we study the multivariate quantitative approximation of real and complex valued continuous multivariate functions on a box or r n n n by the multivariate quasi interpolation hyperbolic tangent neural network operators this approximation is derived by establishing multidimensional jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order partial derivatives our multivariate operators are defined by using a multidimensional density function induced by the hyperbolic tangent function the approximations are pointwise and uniform the related feed forward neural network is with one hidden layer

parameter space structure of continuous time recurrent neural networks a fundamental challenge for any general theory of neural circuits is how to characterize the structure of the space of all possible circuits over a given model neuron as a first step in this direction this letter begins a systematic study of the global parameter space structure of continuous time recurrent neural networks ctrnns a class of neural models that is simple but dynamically universal first we explicitly compute the local bifurcation manifolds of ctrnns we then visualize the structure of these manifolds in net input space for small circuits these visualizations reveal a set of extremal saddle node bifurcation manifolds that divide ctrnn parameter space into regions of dynamics with different effective dimensionality next we completely characterize the combinatorics and geometry of an asymptotically exact approximation to these regions for circuits of arbitrary size finally we show how these regions can be used to calculate estimates of the probability of encountering different kinds of dynamics in ctrnn parameter space

fractional neural network approximation here we study the univariate fractional quantitative approximation of real valued functions on a compact interval by quasi interpolation sigmoidal and hyperbolic tangent neural network operators these approximations are derived by establishing jackson type inequalities involving the moduli of continuity of the right and left caputo fractional derivatives of the engaged function the approximations are pointwise and with respect to the uniform norm the related feed forward neural networks are with one hidden layer our fractional approximation results into higher order converges better than the ordinary ones

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach