fixed time consensus of complex dynamical networks with nonlinear coupling and fuzzy state dependent uncertainties abstract in this paper the fixed time consensus problem for complex dynamical networks with nonlinear coupling and fuzzy state dependent uncertainties is discussed different from most existing publications the controller is designed as a fuzzy logic system which is applicable for complex dynamical networks with system uncertainties and unknown topology to ensure the fixed time consensus furthermore compared with the initial condition based finite time consensus the settling time is bounded by a constant within fixed time regardless of the initial condition based on the lyapunov stability theory and inequality techniques some sufficient criteria for fixed time consensus are obtained finally two numerical examples are granted to display the performance of the obtained results

lapped transforms for efficient transform subband coding two lapped transforms for subband transform coding of signals are introduced a version of the lapped orthogonal transform lot which can be efficiently computed for any transform length and the modulated lapped transform mlt which is based on a modulated quadrature mirror qmf bank the mlt can also be efficiently computed by means of a type iv discrete sine transform dst iv the lot and the mlt are both asymptotically optimal lapped transforms for coding an ar 1 signal with a high intersample correlation coefficient the coding gains of the lot and mlt of length m are higher than that of the discrete cosine transform dct of the same length they are actually close to the coding gains obtained with a dct of length 2m an mlt based adaptive transform coder act for speech signals is simulated the code is essentially free from frame rate noise and has a better spectral resolution that dct based atc systems

optimal control for stochastic nonlinear singular system using neural networks in this paper optimal control for stochastic nonlinear singular system with quadratic performance is obtained using neural networks the goal is to provide optimal control with reduced calculus effort by comparing the solutions of the matrix riccati differential equation mrde obtained from the well known traditional runge kutta rk method and nontraditional neural network method to obtain the optimal control the solution of mrde is computed by feedforward neural network ffnn the accuracy of the solution of the neural network approach to the problem is qualitatively better the advantage of the proposed approach is that once the network is trained it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory the computation time of the proposed method is shorter than the traditional rk method an illustrative numerical example is presented for the proposed method

analysis of the hopf bifurcation for the family of angiogenesis models ii the case of two nonzero unequal delays in this paper we continue the analysis of a family of models with delays describing the process of angiogenesis that is a physiological process involving the growth of new blood vessels from pre existing ones this family of models depends on two time delays and a parameter email protected 0 1 which reflects how strongly the vessels dynamics depends on the ratio between tumour and vessels volume previously in piotrowska and forys 2011 11 we have considered three cases with either one of the delays equals to 0 or both delays equal to each other here we focus on the case with two unequal and non zero delays present in the model and study the dynamics depending on the parameter a including stability switches hopf bifurcation and stability of arising periodic orbits for different email protected 0 1 especially for a 1 and a 0 which reflects the hahnfeldt et al model and d onofrio gandolfi model respectively moreover we consider the influence of constant treatment on the model dynamics it occurs that the treatment not only decreases the tumour size at a steady state but also enlarges the region of stability

channel capacity under sub nyquist nonuniform sampling this paper investigates the effect of sub nyquist sampling upon the capacity of an analog channel the channel is assumed to be a linear time invariant gaussian channel where perfect channel knowledge is available at both the transmitter and the receiver we consider a general class of right invertible time preserving sampling methods which includes irregular nonuniform sampling and characterize in closed form the channel capacity achievable by this class of sampling methods under a sampling rate and power constraint our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal to noise ratio among all spectral sets of measure equal to the sampling rate this can be attained through filterbank sampling with uniform sampling grid employed at each branch with possibly different rates or through a single branch of modulation and filtering followed by uniform sampling these results reveal that for a large class of channels employing irregular nonuniform sampling sets while are typically complicated to realize in practice does not provide capacity gain over uniform sampling sets with appropriate preprocessing our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain in this scenario which is in contrast to the benefits obtained from random mixing in spectrum blind compressive sampling schemes

exponential synchronizationlike criterion for state dependent impulsive dynamical networks this paper focuses on the problem of the exponential synchronizationlike criteria for state dependent impulsive dynamical networks sidns two types of sufficient conditions which are applied to ensure every solution intersecting each impulsive surface exactly once are derived for each type of collision conditions combining with comparison principle and inequality techniques some sufficient conditions are obtained to ensure local exponential synchronizationlike for sidn moreover a quiet different impulsive strategy concerning the trigger rules of impulsive instants is proposed finally an example is given to demonstrate the effectiveness of our results

adaptive filtering in subbands with critical sampling analysis experiments and application to acoustic echo cancellation an exact analysis of the critically subsampled two band modelization scheme is given and it is demonstrated that adaptive cross filters between the subbands are necessary for modelization with small output errors it is shown that perfect reconstruction filter banks can yield exact modelization these results are extended to the critically subsampled multiband schemes and important computational savings are seen to be achieved by using good quality filter banks the problem of adaptive identification in critically subsampled subbands is considered and an appropriate adaptation algorithm is derived the authors give a detailed analysis of the computational complexity of all the discussed schemes and experimentally verify the theoretical results that are obtained the adaptive behavior of the subband schemes that were tested is discussed

efficient reconstruction of band limited sequences from nonuniformly decimated versions by use of polyphase filter banks an efficient polyphase structure for the reconstruction of a band limited sequence from a nonuniformly decimated version is developed theoretically the reconstruction involves the implementation of a bank of multilevel filters and it is shown that how all these reconstruction filters can be obtained at the cost of one mth band low pass filter and a constant matrix multiplier the resulting structure is therefore more general than previous schemes in addition the method offers a direct means of controlling the overall reconstruction distortion t z by appropriate design of a low pass prototype filter p z extension of these results to multiband band limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized along with generalizations to the multidimensional case design examples are included to demonstrate the theory and the complexity of the new method is seen to be much lower than earlier ones

generalized sampling stability and performance analysis generalized sampling provides a general mechanism for recovering an unknown input function f x spl epsiv spl hscr from the samples of the responses of m linear shift invariant systems sampled at 1 mth the reconstruction rate the system can be designed to perform a projection of f x onto the reconstruction subspace v spl phi span spl phi x k sub k spl epsiv z for example the family of bandlimited signals with spl phi x sinc x this implies that the reconstruction will be perfect when the input signal is included in v spl phi the traditional framework of papoulis 1977 generalized sampling theory otherwise one recovers a signal approximation f x spl epsiv v spl phi that is consistent with f x in the sense that it produces the same measurements to characterize the stability of the algorithm we prove that the dual synthesis functions that appear in the generalized sampling reconstruction formula constitute a riesz basis of v spl phi and we use the corresponding riesz bounds to define the condition number of the system we then use these results to analyze the stability of various instances of interlaced and derivative sampling next we consider the issue of performance which becomes pertinent once we have extended the applicability of the method to arbitrary input functions that is when spl hscr is considerably larger than v spl phi and the reconstruction is no longer exact we show that the generalized sampling solution is essentially equivalent to the optimal minimum error approximation we then perform a detailed analysis for the case in which the analysis filters are in l sub 2 and determine all relevant bound constants explicitly finally we use an interlaced sampling example to illustrate these various calculations

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

efficient recovery of sub nyquist sampled sparse multi band signals using reconfigurable multi channel analysis and modulated synthesis filter banks sub nyquist cyclic nonuniform sampling cnus of a sparse multi band signal generates a nonuniformly sampled signal assuming that the corresponding uniformly sampled signal satisfies the nyquist sampling criterion the sequence obtained via cnus can be passed through a reconstructor to recover the missing uniform grid samples at present these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub nyquist sampling in this paper we propose a scheme that reduces the design and implementation complexity of the reconstructor in contrast to the existing reconstructors which use only a multi channel synthesis filter bank fb the proposed reconstructor utilizes both analysis and synthesis fbs which makes it feasitble to achieve an order of magnitude reduction of the complexity the analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts in order to reduce both the design and the implementation complexity of the synthesis fb the synthesis filters are implemented using a cosine modulated fb in addition to the reduced complexity of the reconstructor the proposed multi channel recovery scheme also supports online reconfigurability which is required in flexible multi mode systems where the user subband locations vary with time

perfect reconstruction versus mmse filter banks in source coding classically the filter banks fbs used in source coding schemes have been chosen to possess the perfect reconstruction pr property or to be maximally selective quadrature mirror filters qmfs this paper puts this choice back into question and solves the problem of minimizing the reconstruction distortion which in the most general case is the sum of two terms a first one due to the non pr property of the fb and the other being due to signal quantization in the subbands the resulting filter banks are called minimum mean square error mmse filter banks several quantization noise models are considered first under the classical white noise assumption the optimal positive bit rate allocation in any filter bank possibly nonorthogonal is expressed analytically and an efficient optimization method of the mmse filter banks is derived then it is shown that while in a pr fb the improvement brought by an accurate noise model over the classical white noise one is noticeable it is not the case for the mmse fb the optimization of the synthesis filters is also performed for two measures of the bit rate the classical one which is defined for uniform scalar quantization and the order one entropy measure finally the comparison of rate distortion curves where the distortion is minimized for a given bit rate budget enables us to quantify the snr improvement brought by mmse solutions

magnitude of the truncation error in sampling expansions of band limited signals bounds are established for the truncation error in the sampling theorem for signals with radian bandwidth w w 0 the assumptions are either differenfiability conditions upon the fourier transform of the signal or on the rate of decay of the first derivative of the signal itself finally our theorems are applied to two new examples worked out in detail

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

multirate synchronous sampling of sparse multiband signals recent advances in electro optical systems make them ideal for undersampling multiband signals with very high carrier frequencies in this paper we propose a new scheme for sampling and reconstructing of a multiband sparse signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels the locations of the signal bands are not known a priori the scheme which we call synchronous multirate sampling smrs entails gathering samples synchronously at few different rates whose sum is significantly lower than the nyquist sampling rate the signals are reconstructed by finding a solution of an underdetermined system of linear equations by applying a pursuit algorithm and assuming that the solution is composed of a minimum number of bands the empirical reconstruction success rate is higher than obtained using previously published multicoset scheme when the number of sampling channels is small and the conditions for a perfect reconstruction in the multicoset scheme are not fulfilled the practical sampling system which is simulated in our work consists of three sampling channels our simulation results show that a very high empirical success rate is obtained when the total sampling rate is five times higher than the total signal support of a complex signal with four bands by comparison a multicoset sampling scheme obtains a very high empirical success rate with a total sampling rate which is three times higher than the total signal support however the multicoset scheme requires 14 channels

filter design for mimo sampling and reconstruction we address the problem of finite impulse response fir filter design for uniform multiple input multiple output mimo sampling this scheme encompasses papoulis generalized sampling and several nonuniform sampling schemes as special cases the input signals are modeled as either continuous time or discrete time multiband input signals with different band structures we present conditions on the channel and the sampling rate that allow perfect inversion of the channel additionally we provide a stronger set of conditions under which the reconstruction filters can be chosen to have frequency responses that are continuous we also provide conditions for the existence of fir perfect reconstruction filters and when such do not exist we address the optimal approximation of the ideal filters using fir filters and a minmax l sub 2 end to end distortion criterion the design problem is then reduced to a standard semi infinite linear program an example design of fir reconstruction filters is given

stability and synchronization of discrete time neural networks with switching parameters and time varying delays this paper is concerned with the problems of exponential stability analysis and synchronization of discrete time switched delayed neural networks using the average dwell time approach together with the piecewise lyapunov function technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time delays benefitting from the delay partitioning method and the free weighting matrix technique the conservatism of the obtained results is reduced in addition the decay estimates are explicitly given and the synchronization problem is solved the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

the distribution of sampling rates for signals with equally wide equally spaced spectral bands the distribution of available sampling rates is analysed for a particular type of multiband signal which has bands of equal width centered at harmonics of a fundamental frequency

regularized sampling of multiband signals this paper presents a regularized sampling method for multiband signals that makes it possible to approach the landau limit while keeping the sensitivity to noise and perturbations at a low level the method is based on band limited windowing followed by trigonometric approximation in consecutive time intervals the key point is that the trigonometric approximation inherits the multiband property that is its coefficients are formed by bursts of elements corresponding to the multiband components it is shown that this method can be well combined with the recently proposed synchronous multirate sampling smrs scheme given that the resulting linear system is sparse and formed by ones and zeroes the proposed method allows one to trade sampling efficiency for noise sensitivity and is specially well suited for bounded signals with unbounded energy like those in communications navigation audio systems etc besides it is also applicable to finite energy signals and periodic band limited signals trigonometric polynomials the paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components and the results are validated through several numerical examples

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

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

the eigenvalues of matrices that occur in certain interpolation problems the eigenvalues of the matrices that occur in certain finite dimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots that is on the sampling set we study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the interpolation matrices the bounds can be evaluated in as few as four arithmetic operations and therefore they greatly simplify the assessment of sampling sets regarding numerical stability the accuracy and usefulness of the bounds are illustrated with examples

estimation of time limited channel spectra from nonuniform samples this paper deals with the estimation of a time invariant channel spectrum from its own nonuniform samples assuming there is a bound on the channel s delay spread except for this last assumption this is the basic estimation problem in systems providing channel spectral samples however as shown in the paper the delay spread bound leads us to view the spectrum as a band limited signal rather than the fourier transform of a tapped delay line tdl using this alternative model a linear estimator is presented that approximately minimizes the expected root mean square rms error for a deterministic channel its main advantage over the tdl is that it takes into account the spectrum s smoothness time width thus providing a performance improvement the proposed estimator is compared numerically with the maximum likelihood ml estimator based on a tdl model in pilot assisted channel estimation pace for ofdm

sampling theorems for uniform and periodic nonuniform mimo sampling of multiband signals we examine a multiple input multiple output mimo sampling scheme for a linear time invariant continuous time mimo channel the input signals are modeled as multiband signals with different spectral supports and the channel outputs are sampled on either uniform or periodic nonuniform sampling sets with possibly different but commensurate intervals on the different outputs this scheme encompasses papoulis generalized sampling and several nonuniform sampling schemes as special cases we derive necessary and sufficient conditions on the channel and the sampling rate that allow stable perfect reconstruction of the inputs or equivalently perfect inversion of the channel from an implementation viewpoint we note that it is desirable that the reconstruction filters have continuous frequency responses we derive necessary and sufficient conditions that guarantee this continuity property the frequency responses of the reconstruction filters are specified as solutions to a system of linear equations finally we demonstrate that perfect reconstruction may be possible even when the channel outputs are sampled at an average rate that does not allow the reconstruction of any output from its samples alone in certain instances this average rate can achieve the recently presented fundamental bounds on mimo sampling density

reconstruction of multidimensional bandlimited signals from nonuniform and generalized samples this paper addresses the problem of multidimensional signal reconstruction from nonuniform or generalized samples typical solutions in the literature for this problem utilize continuous filtering the key result of the current paper is a multidimensional interpolation identity which establishes the equivalence of two multidimensional processing operations one of these uses continuous domain filters whereas the other uses discrete processing this result has obvious benefits in the context of the afore mentioned problem the results here expand and generalize earlier work by other authors on the one dimensional 1 d case potential applications include two dimensional 2 d images and video signals

functionally weighted lagrange interpolation of band limited signals from nonuniform samples a modification of the conventional lagrange interpolator is proposed in this paper that allows one to approximate a band limited signal from its own nonuniform samples with high accuracy the modification consists in applying the lagrange method to the signal but pre multiplied by a fixed function and then solving for the desired signal value its efficiency lies in the fact that the fixed function is independent of the sampling instants it is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples for the case in which the sampling instants have a maximum deviation from a uniform grid this paper includes a low complexity recursive implementation of the method its accuracy is validated in the numerical examples by comparison with several interpolators in the literature and by deriving upper and lower bounds for its maximum error

criteria for robust absolute stability of time varying nonlinear continuous time systems the present paper establishes results for the robust absolute stability of a class of nonlinear continuous time systems with time varying matrix uncertainties of polyhedral type and multiple time varying sector nonlinearities by using the variational method and the lyapunov second method criteria for robust absolute stability are obtained in different forms for the given class of systems specifically the parametric classes of lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability the piecewise linear lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases two examples are presented as applications of the present results to a particular second order system and to a specific class of systems with time varying interval matrices in the linear part

stability analysis of markovian jumping stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotical stability analysis problem is considered for a class of markovian jumping stochastic cohen grossberg neural networks cgnns with mixed delays including discrete delays and distributed delays an alternative delay dependent stability analysis result is established based on the linear matrix inequality lmi technique which can easily be checked by utilizing the numerically efficient matlab lmi toolbox neither system transformation nor free weight matrix via newton leibniz formula is required two numerical examples are included to show the effectiveness of the result

selection of observations in signal reconstruction in some signal reconstruction problems the observation equations can be used as a priori information for selecting the best combination of observations before acquiring them in the present correspondence the authors define a selection criterion and propose efficient methods for optimizing the criterion with respect to the combination of observations the examples illustrate the value of optimized sampling using the proposed methods

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

finite horizon h_ infty state estimation for periodic neural networks over fading channels the problem of finite horizon h infty state estimator design for periodic neural networks over multiple fading channels is studied in this paper to characterize the measurement signals transmitted through different channels experiencing channel fading a multiple fading channels model is considered for investigating the situation of correlated fading channels a set of correlated random variables is introduced specifically the channel coefficients are described by white noise processes and are assumed to be correlated two sufficient criteria are provided by utilizing a stochastic analysis approach to guarantee that the estimation error system is stochastically stable and achieves the prescribed h infty performance then the parameters of the estimator are derived by solving recursive linear matrix inequalities finally some simulation results are shown to illustrate the effectiveness of the proposed method

stabilizing effects of impulses in discrete time delayed neural networks this brief studies the global exponential stability of the equilibrium point of discrete time delayed hopfield neural networks dhnns with impulse effects by using difference inequalities we shall consider the stabilizing effects of impulses when the corresponding impulse free dhnn is even not asymptotically stable the obtained results characterize the aggregated effects of impulses and deviation of the impulse free dhnn from its equilibrium point on the exponential stability of the whole system it is shown that because of effects of impulses the impulsive discrete time dhnn may be exponentially stable even if the evolution of impulse free component deviates from its equilibrium point exponentially

mean square exponential stability of stochastic nonlinear delay systems abstractin this paper we are concerned with the stability of stochastic nonlinear delay systems different from the previous literature we aim to show that when the determinate nonlinear delay system is globally exponentially stable the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable in particular we remove the linear growth condition and introduce a new polynomial growth condition for g x t x t t which overcomes the limitation of application scope and the boundedness of diffusion term form finally we provide an example to illustrate our results

on the minimax capacity loss under sub nyquist universal sampling this paper investigates the information rate loss in analog channels when the sampler is designed to operate independent of the instantaneous channel occupancy specifically a multiband linear time invariant gaussian channel under universal sub nyquist sampling is considered the entire channel bandwidth is divided into n subbands of equal bandwidth at each time only k constant gain subbands are active where the instantaneous subband occupancy is not known at the receiver and the sampler we study the information loss through an information rate lossmetric that is the gap of achievable rates caused by the lack of instantaneous subband occupancy information we characterize the minimax information rate loss for the sub nyquist regime provided that the number n of subbands and the snr are both large the minimax limits depend almost solely on the band sparsity factor and the undersampling factor modulo some residual terms that vanish as n and snr grow our results highlight the power of randomized sampling methods i e the samplers that consist of random periodic modulation and low pass filters which are able to approach the minimax information rate loss with exponentially high probability

extended lapped transforms properties applications and fast algorithms the family of lapped orthogonal transforms is extended to include basis functions of arbitrary length within this new family the extended lapped transform elt is introduced as a generalization of the previously reported modulated lapped transform mlt design techniques and fast algorithms for the elt are presented as well as examples that demonstrate the good performance of the elt in signal coding applications therefore the elt is a promising substitute for traditional block transforms in transform coding systems and also a good substitute for less efficient filter banks in subband coding systems

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

the response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation in the first part of this paper we study the properties of a class of linear differential equations with periodic real coefficients and show that the structure of this family of systems guarantees the unstability of the null solution in the second part we use this property to demonstrate that antiangiogenic drugs that act only inhibiting the endothelial cell proliferation might be uneffective in tumor elimination under some relevant biological conditions finally we derive some sufficient criteria that guarantee the disease elimination by therapies using this class of drugs

optimal k space sampling in mrsi for images with a limited region of support magnetic resonance spectroscopic imaging requires a great deal of time to gather the data necessary to achieve satisfactory resolution when the image has a limited region of support ros it is possible to reconstruct the image from a subset of k space samples therefore the authors desire to choose the best possible combination of a small number of k space samples to guarantee the quality of the reconstructed image sequential forward selection sfs is appealing as an optimization method because the previously selected sample can be observed while the next sample is selected however when the number of selected k space samples is less than the number of unknowns at the beginning of the selection process the optimality criterion is undefined and the resulting sfs algorithm cannot be used here the authors present a modified form of the criterion that overcomes this problem and develop an sfs algorithm for the new criterion then the authors develop an efficient computational strategy for this algorithm as well as for the standard sfs algorithm the combined algorithm efficiently selects a reduced set of k space samples from which the ros can be reconstructed with minimal noise amplification

robust exponential stability of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays this paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays and known or unknown parameters the jumping parameters are determined by a continuous time discrete state markov chain and the mixed time delays under consideration comprise both time varying delays and continuously distributed delays to the best of the authors knowledge till now the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper the main objective of this paper is to fill this gap by constructing a novel lyapunov krasovskii functional and using some new approaches and techniques several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square the results presented in this paper generalize and improve many known results finally two numerical examples and their simulations are given to show the effectiveness of the theoretical results

robust patterns in recurrent sampling of multiband signals periodic nonuniform sampling can be used to achieve sub nyquist sampling of bandlimited multiband signals in this paper we examine the question of selecting the sampling pattern in such a scheme so that the reconstruction robustness measured by the condition number of the modulation matrix is maximized contrary to previous work where the sampling pattern was chosen from a discrete set we let the sampling patterns vary continuously but impose a structural constraint using this approach we derive necessary and sufficient conditions on the spectral support of the signal for which perfect conditioning exist namely for which a sampling pattern can be found so that the resulting modulation matrix has a condition number equal to 1 a simple test to check for these conditions is developed and the desired sampling patterns are found an algorithm for choosing the sampling pattern when the aforementioned conditions are not satisfied is also introduced finally we present some simulation results

minimum mean squared error reconstruction for generalized undersampling of cyclostationary processes the generalized sampling problem is considered using a filter bank model with a stochastic process framework a signal reconstruction solution minimizing the time averaged mean squared error is found using a filter bank optimization technique for cyclostationary signals the use of a stochastic model approach to find a minimized error solution rather than a perfect reconstruction solution allows consideration of sampling problems that deterministic approaches cannot solve for instance a particular sampling density is not required allowing reconstruction optimization in cases of undersampling an extension is also presented for optimal reconstruction in the presence of additive noise and interference the result is a generalized sampling model which can be used for an extensive variety of scenarios combining aspects of undersampling multiple input multiple output mimo sampling and periodic nonuniform sampling

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

fundamental distortion limits of analog to digital compression representing a continuous time signal by a set of samples is a classical problem in signal processing we study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bitrate budget to this end we consider a combined sampling and source coding problem in which an analog stationary gaussian signal is reconstructed from its encoded samples these samples are obtained by a set of bounded linear functionals of the continuous time path with a limitation on the average number of samples per unit time given in this setting we provide a full characterization of the minimal distortion in terms of the sampling frequency the bitrate and the signal s spectrum assuming that the signal s energy is not uniformly distributed over its spectral support we show that for each compression bitrate there exists a critical sampling frequency smaller than the nyquist rate such that the distortion in signal reconstruction when sampling at this frequency is minimal our results can be seen as an extension of the classical sampling theorem for bandlimited random processes in the sense that they describe the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples and provide the minimal sampling frequency required in order to achieve this distortion finally we compare the fundamental limits in the combined source coding and sampling problem to the performance of pulse code modulation where each sample is quantized by a scalar quantizer using a fixed number of bits

perfect reconstruction formulas and bounds on aliasing error in sub nyquist nonuniform sampling of multiband signals we examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples this sampling scheme which has been studied previously has an interesting optimality property that uniform sampling lacks one can sample and reconstruct the class spl bscr spl fscr of multiband signals with spectral support spl fscr at rates arbitrarily close to the landau 1969 minimum rate equal to the lebesgue measure of spl fscr even when spl fscr does not tile r under translation using the conditions for exact reconstruction we derive an explicit reconstruction formula we compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band limited to the span of spl fscr the smallest interval containing spl fscr which is a bigger class than the valid signals spl bscr spl fscr band limited to spl fscr we also examine the performance of the reconstruction system when the input contains additive sample noise

optimal sub nyquist nonuniform sampling and reconstruction for multiband signals we study the problem of optimal sub nyquist sampling for perfect reconstruction of multiband signals the signals are assumed to have a known spectral support spl fscr that does not tile under translation such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching landau s 1967 lower bound equal to the measure of spl fscr for signals with sparse spl fscr this rate can be much smaller than the nyquist rate unfortunately the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity in a previous study we derived bounds on the error due to mismodeling and sample additive noise adopting these bounds as performance measures we consider the problems of optimizing the reconstruction sections of the system choosing the optimal base sampling rate and designing the nonuniform sampling pattern we find that optimizing these parameters can improve system performance significantly furthermore uniform sampling is optimal for signals with spl fscr that tiles under translation for signals with nontiling spl fscr which are not amenable to efficient uniform sampling the results reveal increased error sensitivities with sub nyquist sampling however these can be controlled by optimal design demonstrating the potential for practical multifold reductions in sampling rate

design of barycentric interpolators for uniform and nonuniform sampling grids this paper proposes a method to convert a fixed instant interpolator for band limited signals into a variable instant one which has the form of a barycentric interpolator this interpolator makes it possible to approximate the signal and its derivatives with minimal complexity in a range that surrounds the initial instant and is applicable to uniform and nonuniform sampling grids the barycentric form of the interpolator is derived using two different procedures first by the repeated use of bernstein s inequality and taylor s theorem and second by truncating a lagrange type series these procedures show that the proposed method can be applied to existing fixed instant interpolators and that it can be accurate in long time intervals finally an evaluation procedure for barycentric interpolators and their derivatives is presented that minimizes the number of divisions solving at the same time the numerical problems associated with small denominators this paper includes several numerical examples

multidimensional manhattan sampling and reconstruction this paper introduces manhattan sampling in two and higher dimensions and proves sampling theorems for them in 2 d manhattan sampling which takes samples densely along a manhattan grid of lines can be viewed as sampling on the union of two rectangular lattices one dense horizontally and the other vertically with the coarse spacing of each being a multiple of the fine spacing of the other the sampling theorem shows that the images bandlimited to the union of the nyquist regions of the two rectangular lattices can be recovered from their manhattan samples and an efficient procedure for doing so is given such recovery is possible even though there is an overlap among the spectral replicas induced by manhattan sampling in three and higher dimensions there are many possible configurations for manhattan sampling each consisting of the union of special rectangular lattices called bi step lattices this paper identifies them proves a sampling theorem showing that the images bandlimited to the union of the nyquist regions of the bi step rectangular lattices are recoverable from manhattan samples presents an efficient onion peeling procedure for doing so and shows that the union of nyquist regions is as large as any bandlimited region such that all images supported by such can be stably reconstructed from samples taken at the rate of the manhattan sampling it also develops a special representation for the bi step lattices with a number of useful properties while most of this paper deals with continuous space images manhattan sampling of discrete space images is also considered for infinite as well as finite support images

filterbank reconstruction of bandlimited signals from nonuniform and generalized samples this paper introduces a filterbank interpretation of various sampling strategies which leads to efficient interpolation and reconstruction methods an identity which is referred to as the interpolation identity is developed and is used to obtain particularly efficient discrete time systems for interpolation of generalized samples as well as a class of nonuniform samples to uniform nyquist samples either for further processing in that form or for conversion to continuous time the interpolation identity also leads to new sampling strategies including an extension of papoulis 1977 generalized sampling expansion

interpolation of bounded bandlimited signals and applications a method to interpolate a bounded bandlimited signal from its own samples with minimum complexity is presented that guarantees an a priori specified accuracy the method is the result of combining a fast converging sampling expansion with the farrow interpolator technique it provides important complexity reductions in various signal processing applications from which three cases are studied for the farrow interpolator it assures that the interpolation error will be smaller than a known bound both in the time and frequency domains for delay estimation the method allows one to decouple a given estimation detection algorithm in two steps in the first one a few finite convolutions are carried out in order to compute a set of interpolation coefficients in the second the algorithm is executed but with a complexity independent of the length of the temporal observation interval besides it is shown how to introduce this decoupling in the matched filter music and conditional maximum likelihood delay estimators finally the method is employed to give a simple solution to an important efficiency problem in the simulation of communications systems the generation of rayleigh processes

convolution based trigonometric interpolation of band limited signals this paper presents a method to obtain a trigonometric polynomial that accurately interpolates a given band limited signal from a finite sequence of samples the polynomial delivers accurate approximations in the range covered by the sequence except for a short frame close to the range limits besides its accuracy increases exponentially with the frame width the method is based on using a band limited window in order to reduce the truncation error of a convolution series it is shown that the polynomial can be efficiently constructed and evaluated using algorithms designed for the discrete fourier transform dft specifically two basic procedures are presented one based on the fast fourier transform fft and another based on a recursive update algorithm for the short time fft the paper contains three applications the first is a variable fractional delay vfd filter which consists of a short time fft combined with the evaluation of a trigonometric polynomial this filter has low complexity and can be implemented using cordic rotations the second is the interpolation of nonuniform fourier summations where the proposed method eliminates the need to interpolate any kernel sample finally the third can be viewed as a generalization of the fft convolution algorithm and makes it possible to interpolate the output of an finite impulse response fir filter efficiently

reconstruction algorithms in irregular sampling a constructive solution of the irregular sampling problem for band limited functions is given we show how a band limited function can be com pletely reconstructed from any random sampling set whose density is higher than the nyquist rate and give precise estimates for the speed of convergence of this iteration method variations of this algorithm allow for irregular sampling with derivatives reconstruction of band limited functions from local averages and irregular sampling of multivariate band limited functions in the irregular sampling problem one is asked whether and how a band limited function can be completely reconstructed from its irregularly sam pled values f xi this has many applications in signal and image processing seismology meteorology medical imaging etc finding constructive solutions of this problem has received considerable attention among mathematicians and engineers the mathematical literature provides several uniqueness results 1 2 17 18 19 it is now part of the folklore that for stable sampling the sampling rate must be at least the nyquist rate 18 these results as deep as they are have had little impact for the applied sciences because they were not constructive if the sampling set is just a perturbation of the regular oversampling then a reconstruction method has been obtained in a seminal paper by duffin and schaeffer 6 see also 29 if for some l 0 a 0 and o 0 the sampling points xk k e z satisfy a xk ok a k i then the norm equivalence a ir f x 2dx with w n o this norm equivalence implies that it is possible to reconstruct through an iterative procedure the so called frame method most of the later work on constructive methods consists of variations of this method 3 21 22 26 the above conditions on the sampling set exclude random irregular sampling sets e g sets with regions of higher sampling density a partial but undesirable remedy to handle highly irregular sampling sets would be to force the above conditions by throwing away information on part of the points and accept a very slow convergence of the iteration

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

exponential stability on stochastic neural networks with discrete interval and distributed delays this brief addresses the stability analysis problem for stochastic neural networks snns with discrete interval and distributed time varying delays the interval time varying delay is assumed to satisfy 0 d1 d t d2 and is described as d t d 1 h t with 0 h t d 2 d 1 based on the idea of partitioning the lower bound d 1 new delay dependent stability criteria are presented by constructing a novel lyapunov krasovskii functional which can guarantee the new stability conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

global exponential stability of memristive neural networks with mixed time varying delays this article investigates the lagrange exponential stability and the lyapunov exponential stability of memristive neural networks with discrete and distributed time varying delays dmnns by means of inequality techniques theories of the m matrix and the comparison strategy the lagrange exponential stability of the underlying dmnns is considered in the sense of filippov and the globally exponentially attractive set is estimated through employing the m matrix and external input especially when the external input is not concerned the lyapunov exponential stability of the corresponding dmnns is developed immediately in the form of an m matrix which contains some published outcomes as special cases furthermore by constructing an m matrix based differential system the lyapunov exponential stability of the dmnns is studied which is less conservative than some existing ones finally three simulation examples are carried out to examine the validness of the theories

minimum rate sampling and reconstruction of signals with arbitrary frequency support we examine the question of reconstruction of signals from periodic nonuniform samples this involves discarding samples from a uniformly sampled signal in some periodic fashion we give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed we give an implicit characterization of the reconstruction system and a design method by which the ideal reconstruction filters may be approximated we demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing as in earlier work previous work on multiband signals have typically been those for which restrictive assumptions on the sizes and positions of the bands have been made or where the minimum rate was approached asymptotically we show that the class of multiband signals which can be reconstructed exactly is shown to be far larger than previously considered when approaching the minimum rate this freedom allows us in certain cases to have a far less complex reconstruction system

delay dependent stochastic stability of delayed hopfield neural networks with markovian jump parameters in this paper the problem of stochastic stability for a class of time delay hopfield neural networks with markovian jump parameters is investigated the jumping parameters are modeled as a continuous time discrete state markov process without assuming the boundedness monotonicity and differentiability of the activation functions some results for delay dependent stochastic stability criteria for the markovian jumping hopfield neural networks mjdhnns with time delay are developed we establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

common asymptotic behavior of solutions and almost periodicity for discontinuous delayed and impulsive neural networks the paper considers a general neural network model with impulses at a given sequence of instants discontinuous neuron activations delays and time varying data and inputs it is shown that when the neuron interconnections satisfy an m matrix condition or a dominance condition then the state solutions and the output solutions display a common asymptotic behavior as time t it is also shown via a new technique based on prolonging the solutions of the delayed neural network to that it is possible to select a unique special solution that is globally exponentially stable and can be considered as the unique global attractor for the network finally this paper shows that for almost periodic data and inputs the selected solution is almost periodic moreover it is robust with respect to a large class of perturbations of the data analogous results also hold for periodic data and inputs a by product of the analysis is that a sequence of almost periodic impulses is able to induce in the generic case nonstationary almost periodic solutions in an otherwise globally convergent nonimpulsive neural network to the authors knowledge the results in this paper are the only available results on global exponential stability of the unique periodic or almost periodic solution for a general neural network model combining three main features i e impulses discontinuous neuron activations and delays the results in this paper are compared with several results in the literature dealing with periodicity or almost periodicity of some subclasses of the neural network model here considered and some hints for future work are given

an efficient structure for the design of variable fractional delay filters based on the windowing method a variable fractional delay vfd filter is presented that constitutes an efficient alternative to the usual farrow structure the filter is constructed by multiplying the signal to interpolate by a window with proper truncation properties and then applying the sampling theorem the resulting interpolator involves less arithmetic operations than the existing variants of the farrow structure besides if its coefficients are numerically optimized its performance is close to that of the fir equi ripple filter the final part of the correspondence includes a description of the vfd filter implementation corresponding to this interpolator

finite time stability and settling time estimation of nonlinear impulsive systems abstract this paper studies the problem of finite time stability fts for nonlinear impulsive systems based on impulsive control theory several lyapunov based fts theorems involving stabilizing impulses and destabilizing impulses are established respectively our proposed results provide sufficient conditions for estimating the settling time with respect to suitable classes of impulse time sequences it is shown that the settling time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect as compared with the case without using stabilizing impulses a smaller bound of setting time can be derived when a fts system is subject to stabilizing impulses conversely a larger bound of settling time can be derived when the fts system is subject to destabilizing impulses as compared with the case without using destabilizing impulses as a special case we extend the ideas to nonlinear impulsive delay systems and derive some delay independent fts results examples and their simulations are given to demonstrate the applicability of the proposed results

on computing the discrete fourier and cosine transforms an efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms that include the discrete fourier and cosine transform

stability analysis of quaternion valued neural networks with both discrete and distributed delays abstract the existence uniqueness and stability of the equilibrium of quaternion valued neural networks qvnns with both discrete and distributed delays are investigated in this paper the considered model is managed as a single entirety without decomposition based on homeomorphic mapping theorem and linear matrix inequality several sufficient criteria are derived to ascertain the aforementioned qvnns to be globally asymptotically stable and exponentially stable moreover provided criteria can be verified by the linear matrix inequality lmi toolbox in matlab finally one simulation example is demonstrated to verify the effectiveness of obtained results

on an extension of a mathematical model for tumor anti angiogenesis abstract we describe the optimal synthesis of controlled trajectories for a mathematical model for tumor anti angiogenesis when natural growth and death of the endothelial support are included in the modeling the admissibility of an optimal singular arc that forms the center piece for this synthesis is investigated depending on a parameter that denotes the net rate of these effects on the carrying capacity of the vasculature

exponential stability in p th mean of solutions and of convergent euler type solutions of stochastic delay differential equations one concept of the stability of a solution of an evolutionary equation relates to the sensitivity of the solution to perturbations in the initial data there are other stability concepts notably those concerned with persistent perturbations results are presented on the stability in p th mean of solutions of stochastic delay differential equations with multiplicative noise and of stochastic delay difference equations the difference equations are of a type found in numerical analysis and we employ our results to obtain mean square stability criteria for the solution of the euler maruyama discretization of stochastic delay differential equations the analysis proceeds as follows we show that an inequality of halanay type derivable via comparison theory can be employed to derive conditions for p th mean stability of a solution we then produce a discrete analogue of the halanay type theory that permits us to develop a p th mean stability analysis of analogous stochastic difference equations the application of the theoretical results is illustrated by deriving mean square stability conditions for solutions and numerical solutions of a constant coefficient linear test equation