continuous time additive hopfield type neural networks with impulses we investigate the global stability characteristics of a system of equations modelling the dynamics of additive hopfield type neural networks with impulses in the continuous time case

the method of lyapunov functionals and exponential stability of impulsive systems with time delay abstract this paper studies exponential stability of impulsive systems with time delay by employing the method of lyapunov functionals several exponential stability criteria are established our results have improved and generalized some of the known results found in the literature several examples are also discussed to illustrate our results

multistability of second order competitive neural networks with nondecreasing saturated activation functions in this paper second order interactions are introduced into competitive neural networks nns and the multistability is discussed for second order competitive nns socnns with nondecreasing saturated activation functions firstly based on decomposition of state space cauchy convergence principle and inequality technique some sufficient conditions ensuring the local exponential stability of 2n equilibrium points are derived secondly some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region thirdly the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the socnns can have r 1 n locally exponentially stable equilibrium points even if there is no second order interactions the obtained results are less restrictive than those in some recent works finally three examples with their simulations are presented to verify the theoretical analysis

stability of statistical properties in two dimensional piecewise hyperbolic maps we investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions we accomplish such a program in the case of two dimensional maps with uniformly bounded second derivative but we are confident that the present approach can be successful in much greater generality we hope including higher dimensional billiards for the class of systems at hand we obtain a complete description of the srb measures their statistical properties and their stability with respect to many types of perturbations including deterministic and random perturbations and holes

generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

mmse based mdl method for robust estimation of number of sources without eigendecomposition it is well known that the conventional eigenvalue based minimum description length mdl approach for source number estimation suffers from high computational load and performs optimally only in the presence of spatially and temporally white noise to improve the robustness of the mdl methodology we propose to utilize the minimum mean square error mmse of the multistage wiener filter to calculate the required description length for encoding the observed data instead of relying on the eigenvalues of the data covariance matrix as there is no need to calculate the covariance matrix and its eigenvalue decomposition our derived mmse based mdl mmdl method is also more computationally efficient than the traditional counterparts numerical examples are included to demonstrate the robustness of the mmdl detector in nonuniform noise

model order selection for complex sinusoids in the presence of unknown correlated gaussian noise we consider the problem of detecting and estimating the amplitudes and frequencies of an unknown number of complex sinusoids based on noisy observations from an unstructured array in parametric detection problems like this information theoretic criteria such as minimum description length mdl and akaike information criterion aic have previously been used for joint detection and estimation in our paper model selection based on extreme value theory evt which has previously been used for enumerating real sinusoidal components from one dimensional observations is generalized to the case of multidimensional complex observations in the presence of noise with an unknown spatial correlation matrix unlike the previous work the likelihood ratios considered in the mutlidimensional case cannot be addressed using gaussian random fields instead chi square random fields associated with the generalized likelihood ratio test are encountered and evt is used to analyze the model order overestimation probability for a general class of likelihood penalty terms including mdl and aic and a novel likelihood penalty term derived based on evt since the exact evt penalty term involves a lambert w function an approximate penalty term is also derived that is more tractable we provide threshold signal to noise ratios snrs and show that the model order underestimation probability is asymptotically vanishing for evt and mdl we also show that mdl and evt are asymptotically consistent while aic is not and that with finite samples the detection performance of evt outperforms mdl and aic finally the accuracy of the derived threshold snrs is also demonstrated

detection and estimation of doa s of signals via bayesian predictive densities a new criterion based on bayesian predictive densities and subspace decomposition is proposed for simultaneous detection of signals impinging on a sensor array and estimation of their direction of arrivals doas the solution is applicable for both coherent and noncoherent signals and an arbitrary array geometry the proposed detection criterion is strongly consistent and outperforms the mdl and aic criteria particularly for a small number of sensors and or snapshots and or low snr without increased computational complexity when the prior of the direction of arrival is a uniform distribution the bayesian estimator for the directional parameters coincides with the unconditional maximum likelihood estimator simulation results that demonstrate the performance of the proposed solution are included

a new adaptive backpropagation algorithm based on lyapunov stability theory for neural networks a new adaptive backpropagation bp algorithm based on lyapunov stability theory for neural networks is developed in this paper it is shown that the candidate of a lyapunov function v k of the tracking error between the output of a neural network and the desired reference signal is chosen first and the weights of the neural network are then updated from the output layer to the input layer in the sense that deltav k v k v k 1 0 the output tracking error can then asymptotically converge to zero according to lyapunov stability theory unlike gradient based bp training algorithms the new lyapunov adaptive bp algorithm in this paper is not used for searching the global minimum point along the cost function surface in the weight space but it is aimed at constructing an energy surface with a single global minimum point through the adaptive adjustment of the weights as the time goes to infinity although a neural network may have bounded input disturbances the effects of the disturbances can be eliminated and asymptotic error convergence can be obtained the new lyapunov adaptive bp algorithm is then applied to the design of an adaptive filter in the simulation example to show the fast error convergence and strong robustness with respect to large bounded input disturbances

an analogue of the prime number theorem for closed orbits of axiom a flows for an axiom a flow restricted to a basic set we extend the zeta function to an open set containing w s h where h is the topological entropy this enables us to give an asymptotic formula for the number of closed orbits by adapting the wiener ikehara proof of the prime number theorem

exponential stability of impulsive high order hopfield type neural networks with time varying delays this paper considers the problems of global exponential stability and exponential convergence rate for impulsive high order hopfield type neural networks with time varying delays by using the method of lyapunov functions some sufficient conditions for ensuring global exponential stability of these networks are derived and the estimated exponential convergence rate is also obtained as an illustration an numerical example is worked out using the results obtained

iterative methods for subspace and doa estimation in nonuniform noise usually direction of arrival doa estimators are derived under the assumption of uniform white noise whose covariance matrix is a scaled identity matrix however in practice the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix in this situation the performance of doa estimators may be deteriorated considerably if the noise nonuniformity is ignored to tackle this problem iterative approaches to subspace estimation are developed and the corresponding subspace based doa estimators are addressed in our proposed methods the signal subspace and noise covariance matrix are first determined by maximizing the log likelihood ll function or solving a least squares ls minimization problem both of which are accomplished in an iterative manner then the doas are determined from the subspace estimate and or noise covariance matrix estimate with the help of traditional doa estimators as the signal subspace and noise covariance matrix can be computed in closed form in each iteration the proposals are computationally attractive furthermore the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold enabling us to handle array uncertainties by incorporating conventional subspace based calibration algorithms simulations and experimental results are included to demonstrate the superiority of the proposed approaches

open billiards invariant and conditionally invariant probabilities on cantor sets billiards are the simplest models for understanding the statistical theory of the dynamics of a gas in a closed compartment we analyze the dynamics of a class of billiards the open billiard on the plane in terms of invariant and conditionally invariant probabilities the dynamical system has a horseshoe structure the stable and unstable manifolds are analytically described the natural probability mu is invariant and has support in a cantor set this probability is the conditional limit of a conditional probability mu f that has a density with respect to the lebesgue measure a formula relating entropy lyapunov exponent and hausdorff dimension of a natural probability mu for the system is presented the natural probability mu is a gibbs state of a potential psi cohomologous to the potential associated to the positive lyapunov exponent see formula 0 1 and we show that for a dense set of such billiards the potential tb is not lattice as the system has a horseshoe structure

detection and localization of multiple sources via the stochastic signals model a method for the detection of coherent and noncoherent signals based on the application of j rissanen s 1978 minimum description length principle for model selection to the stochastic signals model is presented the detection and localization are done simultaneously with the location estimator coinciding with the maximum likelihood estimator derived by j f bohme 1986 the proposed method outperforms the method of m wax and i ziskind 1989 especially in the threshold region simulation results demonstrating the improved performance are included

analysis of the performance and sensitivity of eigendecomposition based detectors a new framework is presented for the analysis of the performance of detection methods such as aic and mdl which are based on the eigenvalues of the sample covariance matrix it is shown that theoretical analysis of the probabilities of overestimation and underestimation can be much more conveniently carried out via a proposed particularly simple sequence of statistics also the breakdown of these detection methods in the presence of model nonidealities is explored by theory simulations and experimentation with real array data for example theoretical arguments are given to demonstrate the high degree of sensitivity of the detectors to unknown deviations of the noise from whiteness

on the rate of convergence to equilibrium in one dimensional systems we determine the essential spectral radius of the perron frobenius operator for piecewise expanding transformations considered as an operator on the space of functions of bounded variation and relate the speed of convergence to equilibrium in such one dimensional systems to the greatest eigenvalues of generalized perron frobenius operators of the transformations operators which yield singular invariant measures

locating resonances for axiom a dynamical systems for a class of differentiable dynamical systems called axiom a systems it has been shown by pollicott and the author that correlation functions have fourier transforms which are meromorphic in a strip the poles or resonances are however not easy to locate this note reviews the results which are known and discusses a simple model where the position of resonances can be estimated the effect of noise is also discussed

estimation of the number of sources in unbalanced arrays via information theoretic criteria estimating the number of sources impinging on an array of sensors is a well known and well investigated problem a common approach for solving this problem is to use an information theoretic criterion such as minimum description length mdl or the akaike information criterion aic the mdl estimator is known to be a consistent estimator robust against deviations from the gaussian assumption and nonrobust against deviations from the point source and or temporally or spatially white additive noise assumptions over the years several alternative estimation algorithms have been proposed and tested usually these algorithms are shown using computer simulations to have improved performance over the mdl estimator and to be robust against deviations from the assumed spatial model nevertheless these robust algorithms have high computational complexity requiring several multidimensional searches in this paper which is motivated by real life problems a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken an mdl type estimator that is robust against deviation from assumption of equal noise level across the array is studied the consistency of this estimator even when deviations from the equal noise level assumption occur is proven a novel low complexity implementation method avoiding the need for multidimensional searches is presented as well making this estimator a favorable choice for practical applications

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

estimation of the directions of arrival of signals in unknown correlated noise i the map approach and its implementation the authors propose a method of direction of arrival doa estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary other than being positive definite they examine the projection of the data onto the noise subspace the conditional probability density function pdf of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed the a posteriori pdf of the signal parameters alone is then obtained by assigning a noninformative a priori pdf to the unknown noise covariance matrix and integrating out this quantity a simple criterion for the maximum a posteriori map estimate of the doas of the signals is established some properties of this criterion are discussed and an efficient numerical algorithm for the implementation of this criterion is developed the advantage of this method is that the noise covariance matrix does not have to be known nor must it be estimated

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

universal coding information prediction and estimation a connection between universal codes and the problems of prediction and statistical estimation is established a known lower bound for the mean length of universal codes is sharpened and generalized and optimum universal codes constructed the bound is defined to give the information in strings relative to the considered class of processes the earlier derived minimum description length criterion for estimation of parameters including their number is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings it is also shown that one cannot do prediction in gaussian autoregressive moving average arma processes below a bound which is determined by the information in the data

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

source enumeration via mdl criterion based on linear shrinkage estimation of noise subspace covariance matrix numerous methodologies have been investigated for source enumeration in sample starving environments for those having their root in the framework of random matrix theory the involved distribution of the sample eigenvalues is required instead of relying on the eigenvalue distribution this work devises a linear shrinkage based minimum description length ls mdl criterion by utilizing the identity covariance matrix structure of noise subspace components with linear shrinkage and gaussian assumption of the observations an accurate estimator for the covariance matrix of the noise subspace components is derived the eigenvalues obtained from the estimator turn out to be a linear function of the corresponding sample eigenvalues enabling the ls mdl criterion to accurately detect the source number without incurring significantly additional computational load furthermore the strong consistency of the ls mdl criterion for m n and m n c 0 is proved where m and n are the antenna number and snapshot number respectively simulation results are included for illustrating the effectiveness of the proposed criterion

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

absolutely continuous invariant measures for expanding piecewise linear maps we prove the existence of absolutely continuous invariant measures for arbitrary expanding piecewise linear maps on bounded polyhedral domains in euclidean spaces d

detection estimation of more uncorrelated gaussian sources than sensors in nonuniform linear antenna arrays ii partially augmentable arrays previous studies dealing with direction of arrival doa estimation for uncorrelated planes waves incident on nonuniform m sensor arrays assumed that the number of signal sources m was known or had already been estimated in the conventional case m m traditional detection techniques such as akaike s information criterion aic and minimum description length mdl that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied although we demonstrate that these results can be misleading for nonuniform arrays in the superior case m spl ges m these standard techniques are not applicable we introduce a new approach to the detection problem for fully augmentable arrays whose set of intersensor differences is complete we show that the well known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting toeplitz matrix is generally not positive definite for realistic sample volumes we propose a transformation of this augmented matrix into a positive definite toeplitz matrix t sub spl mu with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources spl mu comparison of the results of these best fit transformations over the permissible range of candidates then allows us to select the most likely number of sources m spl circ using traditional criteria and yields uniquely defined doas simulation results demonstrate the high performance of this method since detection techniques for superior scenarios have not been previously described in the literature we compare our method with the standard aic and mdl techniques in a conventional case with similar cramer rao bound crb and find that it has a similar detection performance

global dynamics of hopfield neural networks involving variable delays abstract in this article a model describing dynamics of hopfield neural networks involving variable delays is considered existence and uniqueness of the equilibrium point under fairly general and easily verifiable conditions are also established further we derive sufficient criteria of global asymptotic stability gas of the equilibrium point

robust properties of likelihood ratio tests summary the usual asymptotic chi squared distribution for the likelihood ratio test statistic is based on the assumptions that the data come from the parametric model under consideration and that the parameter satisfies the null hypothesis in this paper we examine the distribution of the likelihood ratio statistic when the data do not come from the parametric model but when the nearest member of the parametric family still satisfies the null hypothesis in general the likelihood ratio statistic no longer follows an asymptotic chi squared distribution and an alternative statistic based on the unionintersection approach is proposed

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

absolutely continuous invariant measures for piecewise real analytic expanding maps on the plane we prove the existence of absolutely continuous invariant measures for piecewise real analytic expanding maps on bounded regions in the plane

exponential stability of high order bidirectional associative memory neural networks with time delays in this paper exponential stability is studied for a class of high order bidirectional associative memory bam neural networks with time delays by employing the linear matrix inequality lmi and the lyapunov functional methods several sufficient conditions are obtained for ensuring the system to be globally exponentially stable two illustrative examples are also given in the end of this paper to show the effectiveness of our results

source number estimators using transformed gerschgorin radii we introduce effective uses of gerschgorin radii of the unitary transformed covariance matrix for source number estimation there are two approaches likelihood and heuristic used for developing the detection criteria the likelihood approach combines the gerschgorin radii to the well known source number detectors and improves their detection performances for gaussian and white noise processes it is verified that the gerschgorin likelihood estimators gle are consistent the gerschgorin aic yields a consistent estimate and the gerschgorin mdl criterion does not tend to underestimate for small or moderate data samples the heuristic approach applying the gerschgorin disk estimator gde developed from the projection concept overcomes the problem in cases of small data samples an unknown noise model and data dependency furthermore the detection performances of both approaches through the suggested rotations and averaging can be further improved finally the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

impulsive control and synchronization for delayed neural networks with reaction diffusion terms this paper discuss the global exponential stability and synchronization of the delayed reaction diffusion neural networks with dirichlet boundary conditions under the impulsive control in terms of p norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction diffusion neural networks with dirichlet boundary conditions some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed finally some numerical examples are given to demonstrate the effectiveness of the proposed control methods

resonances for axiom bf a flows etant donne un flot d axiome a sur m et des fonctions lisses b c m r on montre que la fonction de correlation en temps bc pour un etat de gibbs a une transformee de fourier bc mesomorphe dans une bande on etudie les residus des poles de bc

fractional hopfield neural networks fractional dynamic associative recurrent neural networks this paper mainly discusses a novel conceptual framework fractional hopfield neural networks fhnn as is commonly known fractional calculus has been incorporated into artificial neural networks mainly because of its long term memory and nonlocality some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer order neural networks therefore it is naturally makes one ponder how to generalize the first order hopfield neural networks to the fractional order ones and how to implement fhnn by means of fractional calculus we propose to introduce a novel mathematical method fractional calculus to implement fhnn first we implement fractor in the form of an analog circuit second we implement fhnn by utilizing fractor and the fractional steepest descent approach construct its lyapunov function and further analyze its attractors third we perform experiments to analyze the stability and convergence of fhnn and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting the main contribution of our work is to propose fhnn in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach construct its lyapunov function prove its lyapunov stability analyze its attractors and apply fhnn to the defense against chip cloning attacks for anticounterfeiting a significant advantage of fhnn is that its attractors essentially relate to the neuron s fractional order fhnn possesses the fractional order stability and fractional order sensitivity characteristics

a delayed projection neural network for solving linear variational inequalities in this paper a delayed projection neural network is proposed for solving a class of linear variational inequality problems the theoretical analysis shows that the proposed neural network is globally exponentially stable under different conditions by the proposed linear matrix inequality lmi method the monotonicity assumption on the linear variational inequality is no longer necessary by employing lagrange multipliers the proposed method can resolve the constrained quadratic programming problems finally simulation examples are given to demonstrate the satisfactory performance of the proposed neural network

input to state stability of impulsive and switching hybrid systems with time delay this paper investigates input to state stability iss and integral input to state stability iiss of impulsive and switching hybrid systems with time delay using the method of multiple lyapunov krasovskii functionals it is shown that even if all the subsystems governing the continuous dynamics in the absence of impulses are not iss iiss impulses can successfully stabilize the system in the iss iiss sense provided that there are no overly long intervals between impulses i e the impulsive and switching signal satisfies a dwell time upper bound condition moreover these impulsive iss iiss stabilization results can be applied to systems with arbitrarily large time delays conversely in the case when all the subsystems governing the continuous dynamics are iss iiss in the absence of impulses the iss iiss properties can be retained if the impulses and switching do not occur too frequently i e the impulsive and switching signal satisfies a dwell time lower bound condition several illustrative examples are presented with their numerical simulations to demonstrate the main results

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

source enumeration for high resolution array processing using improved gerschgorin radii without eigendecomposition accurate detection of sources with low complexity is of considerable interest in practical applications of high resolution array processing this paper addresses a new computationally efficient method for source enumeration by using enhanced gerschgorin radii without eigendecompositofion the proposed method can calculate the gerschgorin radii in a more efficient manner in which the additive background noise can be efficiently suppressed and the computational complexity can be considerably reduced therefore the method is more accurate and computationally attractive furthermore the method does not rely on the eigenvalues of a covariance matrix or the signal noise power making it robust against deviations from the assumption of spatially white noise model numerical results are presented to demonstrate the performance of the method

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

rank estimation and redundancy reduction of high dimensional noisy signals with preservation of rare vectors in this paper we address the problem of redundancy reduction of high dimensional noisy signals that may contain anomaly rare vectors which we wish to preserve for example when applying redundancy reduction techniques to hyperspectral images it is essential to preserve anomaly pixels for target detection purposes since rare vectors contribute weakly to the norm of the signal as compared to the noise based criteria are unsatisfactory for obtaining a good representation of these vectors the proposed approach combines and norms for both signal subspace and rank determination and considers two aspects one aspect deals with signal subspace estimation aiming to minimize the maximum of data residual norms denoted as for a given rank conjecture the other determines whether the rank conjecture is valid for the obtained signal subspace by applying extreme value theory results to model the distribution of the noise norm these two operations are performed alternately using a suboptimal greedy algorithm which makes the proposed approach practically plausible the algorithm was applied on both synthetically simulated data and on a real hyperspectral image producing better results than common based methods

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

no or infinitely many a c i p for piecewise expanding cr maps in higher dimensions we modify tsujii s example 9 to show that in contrast with the one dimensional case piecewise uniformly expanding and c r maps of the plane may

on stability in terms of two measures for impulsive systems of functional differential equations this paper considers the stability problem for a class of impulsive systems of functional differential equations by using lyapunov functions and the razumikhin technique several stability criteria in terms of two measures are established some examples are worked out to illustrate the theorems

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

impulsive stabilization of functional differential equations via liapunov functionals abstract in this paper we consider the impulsive stabilization problems for a class of impulsive functional differential equation of the form x t f t x t t t 0 x i k t x t t t k k z our method is based on the application of the liapunov second method together with liapunov functionals

statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing the performances of the akaike 1974 information criterion and the minimum descriptive length criterion methods are examined the events which lead to erroneous decisions are considered and on the basis of these events the probabilities of error for the two criteria are derived the probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated hermitian matrix it is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation although the derivation of the probabilities of error is based on an asymptotic analysis the results are confirmed to be in very close agreement with computer simulation results

independent component analysis based source number estimation and its comparison for mechanical systems abstract it has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori in this paper we propose a novel source number estimation based on independent component analysis ica and clustering evaluation analysis we investigate and benchmark three information based source number estimations akaike information criterion aic minimum description length mdl and improved bayesian information criterion ibic all the above methods are comparatively studied in both numerical and experimental case studies with typical mechanical signals the results demonstrate that the proposed ica based source number estimation with nonlinear dissimilarity measures performs more stable and robust than the information based ones for mechanical systems

on stabilization of stochastic cohen grossberg neural networks with mode dependent mixed time delays and markovian switching the globally exponential stabilization problem is investigated for a general class of stochastic cohen grossberg neural networks with both markovian jumping parameters and mixed mode dependent time delays the mixed time delays consist of both discrete and distributed delays this paper aims to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive delay dependent criteria for the exponential stabilization problem three numerical examples are carried out to demonstrate the feasibility of our delay dependent stabilization criteria

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

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

exponential stability for impulsive delay differential equations by razumikhin method abstract in this paper we study exponential stability for impulsive delay differential equation of the form x t f t x t t t k x t i k t x t t t k k n by employing the razumikhin technique and lyapunov functions several exponential stability criteria are established some examples are also discussed to illustrate our results

global asymptotic stability of high order hopfield type neural networks with time delays abstract this paper studies the problem of global asymptotic stability of a class of high order hopfield type neural networks with time delays by utilizing lyapunov functionals we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality lmi numerical examples are given to illustrate the advantages of our approach

source enumeration in array processing using a two step test we investigate the problem of enumerating source signals impinging on an array of sensors given noisy limited observations the assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size in this paper we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two step test numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes

detection of sources using bootstrap techniques source detection in array processing can be viewed as a test for equality of eigenvalues such a test is proposed based on a multiple test procedure that considers all pairwise comparisons between eigenvalues using the bootstrap to estimate the null distributions of the test statistics results in a procedure with minimal assumptions on the nature of the signal simulations show that the proposed test is superior to information theoretic criteria such as the mdl which are based on gaussian signals and large sample sizes performance in most cases exceeds the more powerful sphericity test

detection of signals by information theoretic criteria general asymptotic performance analysis detecting the number of sources is a well known and a well investigated problem in this problem the number of sources impinging on an array of sensors is to be estimated the common approach for solving this problem is to use an information theoretic criterion like the minimum description length mdl or the akaike information criterion aic although it has been gaining much popularity and has been used in a variety of problems the performance of information theoretic criteria based estimators for the unknown number of sources has not been sufficiently studied yet in the context of array processing the performance of such estimators were analyzed only for the special case of gaussian sources where no prior knowledge of the array structure if given is used based on the theory of misspecified models this paper presents a general asymptotic analysis of the performance of any information theoretic criterion based estimator and especially of the mdl estimator in particular the performance of the mdl estimator which assumes gaussian sources and structured array when applied to gaussian sources is analyzed in addition it is shown that the performance of a certain mdl estimator is not very sensitive to the actual distribution of the source signals however appropriate use of prior knowledge about the array geometry can lead to significant improvement in the performance of the mdl estimator simulation results show a good fit between the empirical and the theoretical results

consensus of second order multi agent systems via impulsive control using sampled hetero information in this paper the consensus problem for second order multi agent systems using impulsive control with sampled hetero information is investigated necessary and sufficient conditions for sampling interval to achieve consensus for the second order multi agent systems are obtained analysis for the upper bound of sampling interval convergence performance and communication cost of the proposed control protocols are also discussed some numerical examples are given to demonstrate the effectiveness of the proposed control protocols

on the use of order statistics for improved detection of signals by the mdl criterion the minimum description length mdl criterion for model selection has been successfully applied to the problem of estimating the number of sources in noise we show that by employing an order statistics approach in the existing solution a new processor with uniformly improved performance is constructed at the cost of greater complexity we prove that the resulting mdl based processor is consistent results of simulations of practical scenarios of interest demonstrate how significant the performance improvement can be

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed