stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

delay dependent robust hbox it h _ infty control for uncertain discrete time fuzzy systems with time varying delays this paper deals with the robust h infin control problem for discrete time takagi sugeno t s fuzzy systems with norm bounded parametric uncertainties and interval time varying delays first based on a new lyapunov functional we present a sufficient condition guaranteeing that the resulting closed loop system is robustly stable and satisfies a prescribed h infin performance level the lyapunov functional used here depends on not only the fuzzy basis function but on the lower and upper bounds of the time varying delay as well second two classes of delay dependent conditions for the existence of the concerned h infin fuzzy controllers are given in terms of relaxed linear matrix inequalities lmis and a desired controller can be designed by using the solutions to these lmis finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

observer based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation this paper studies the problem of adaptive output tracking control for a class of nonlinear systems subject to unknown time delay and input saturation to address the delay and the input saturation some reasonable assumptions and an auxiliary system are introduced the fuzzy logic approach is employed to approximate the unknown functions in the system an observer is designed to estimate the unavailable system states the dynamic surface control dsc technique is utilized to avoid the problem of explosion of complexity by combining the backstepping and dsc methods a bounded control input is designed to ensure that all signals of the closed loop system are bounded and the tracking error can fluctuate around the origin within a small neighborhood finally two examples are presented to demonstrate the effectiveness and potential of the proposed new design techniques

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

a model containing both the camassa holm and degasperis procesi equations abstract a nonlinear dispersive partial differential equation which includes the famous camassa holm and degasperis procesi equations as special cases is investigated although the h 1 norm of the solutions to the nonlinear model does not remain constants the existence of its weak solutions in lower order sobolev space h s with 1 s 3 2 is established under the assumptions u 0 h s and u 0 x l the local well posedness of solutions for the equation in the sobolev space h s r with s 3 2 is also developed

multiframe temporal estimation of cardiac nonrigid motion a robust flexible system for tracking the point to point nonrigid motion of the left ventricular lv endocardial wall in image sequences has been developed this system is unique in its ability to model motion trajectories across multiple frames the foundation of this system is an adaptive transversal filter based on the recursive least squares algorithm this filter facilitates the integration of models for periodicity and proximal smoothness as appropriate using a contour based description of the object s boundaries a set of correspondences between contours and an associated set of correspondence quality measures comprise the input to the system frame to frame relationships from two different frames of reference are derived and analyzed using synthetic and actual images two multiframe temporal models both based on a sum of sinusoids are derived illustrative examples of the system s output are presented for quantitative analysis validation of the system is performed by comparing computed trajectory estimates with the trajectories of physical markers implanted in the lv wall sample case studies of marker trajectory comparisons are presented ensemble statistics from comparisons with 15 marker trajectories are acquired and analyzed a multiframe temporal model without spatial periodicity constraints was determined to provide excellent performance with the least computational cost a multiframe spatiotemporal model provided the best performance based on statistical standard deviation although at significant computational expense

a minimal parameter adaptive notch filter with constrained poles and zeros a new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow band or sine wave signals in an additive broad band process the algorithm is of recursive prediction error rpe form and uses a special constrained model of infinite impulse response iir with a minimal number of parameters the convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape for sufficiently large data sets the variances of the sine wave frequency estimates are of the same order of magnitude as the cramer rao bound results from simulations illustrate the performance of the algorithm under a wide range of conditions

the recursive companion matrix root tracker a new sequential o n sup 2 polynomial factorization algorithm that updates all roots of an nth order polynomial with real time varying coefficients simultaneously and efficiently in response to coefficient perturbations is introduced the algorithm is based on a variant of sequential orthogonal iteration and exploits the special structure of the coefficient companion matrix all internal operations are based on real passive givens plane rotations and real matrix vector multiplications the algorithm is unconditionally stable and requires no initial guess of the root values numerical examples are presented to demonstrate the performance of the algorithm comparisons are made to the starer and nehorai 1991 root tracking algorithm

principal decomposition of time frequency distributions the authors present a novel time frequency analysis technique which uses principal components analysis to map any given time frequency distribution tfd of a signal into a set of three 1 d principal decomposition functions these three functions may then be considered to be separable components of a time frequency function which they refer to as the principal approximation function for the original tfd they show how principal decomposition analysis is useful for the enhancement and frequency tracking of nonstationary harmonic signals

a neural root finder of polynomials based on root moments this letter proposes a novel neural root finder based on the root moment method rmm to find the arbitrary roots including complex ones of arbitrary polynomials this neural root finder nrf was designed based on feedforward neural networks fnn and trained with a constrained learning algorithm cla specifically we have incorporated the a priori information about the root moments of polynomials into the conventional backpropagation algorithm bpa to construct a new cla the resulting nrf is shown to be able to rapidly estimate the distributions of roots of polynomials we study and compare the advantage of the rmm based nrf over the previous root coefficient method based nrf and the traditional muller and laguerre methods as well as the mathematica roots function and the behaviors the accuracies of the resulting root finders and their training speeds of two specific structures corresponding to this fnn root finder the log and the fnn we also analyze the effects of the three controlling parameters p0 p with the cla on the two nrfs theoretically and experimentally finally we present computer simulation results to support our claims

traveling wave solutions of the camassa holm equation all weak traveling wave solutions of the camassa holm equation are classified we show that in addition to smooth solutions there are a multitude of traveling waves with singularities peakons cuspons stumpons and composite waves

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

conditional mean and maximum likelihood approaches to multiharmonic frequency estimation the performance of an extended kalman filter ekf applied to the problem of estimating the assumed constant parameters fundamental frequency harmonic phases and amplitudes of a complex multiharmonic signal measured in noise is shown to be asymptotically i e as the number of measurements tends to infinity efficient the cramer rao cr bounds associated with the estimation problem are derived for the case where the measurements commence at an arbitrary time distinct from zero

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

estimating the parameters of general frequency modulated signals a general frequency modulated gfm signal characterizes the vibrations produced by compressors turbines propellers gears and other rotating machines in a dynamic environment a gfm signal is defined as the composition of a real or complex periodic or almost periodic carrier function with a real differentiable modulation function a gfm signal therefore contains sinusoids whose frequencies are possibly nonintegral multiples of a fundamental to distinguish a gfm signal from a set of unrelated sinusoids it is necessary to track them as a group this paper develops the general frequency modulation tracker gfmt for one or more gfm signals in noise using the expectation conditional maximization ecm algorithm that is an extension of the expectation maximization em algorithm three advantages of this approach are that the ratios harmonic numbers of the carrier functions do not need to be known a priori that the parameters of multiple signals are estimated simultaneously and that the gfmt algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required several simulated examples are presented to illustrate the algorithm s performance

new speech harmonic structure measure and its applications to speech processing the harmonic structure can be easily recognized in time frequency representation of speech signals in adverse environment the harmonicity is a measure of the completeness of a harmonic structure this paper presents a new harmonic structure measure that extends the conventional harmonicity to a set of harmonicities they are expressed in terms of the grid harmonicity the temporal harmonicity the segment spectral harmonicity and the segmental harmonicity the grid harmonicity measures the completeness of individual harmonics in each frame the grid harmonicities in a frame are summed up to form a temporal harmonicity for representing the strength of harmonicity the segment spectral harmonicity computed by summing specific grid harmonicity over a segment evaluates the integrity of individual harmonics across a segment the segmental harmonicity evaluates the total strength of harmonic structure within a segment this set of harmonicities is available for a systematic analysis of the harmonic structure and effective to several speech processing tasks the applications to speech distortion analysis robust fundamental frequency estimation robust voicing detection and speech enhancement are demonstrated

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

a recursive maximum likelihood algorithm for arma line enhancement optimal filtering of narrow band signals corrupted by noise requires an infinite impulse response iir filter a recursive maximum likelihood algorithm is proposed for adaptively adjusting the coefficients of an iir line enhancer the performance of this adaptive iir filter is analyzed and compared to that of a finite impulse response filter preliminary simulation results are presented to illustrate the behavior of the proposed algorithm under various signal to noise conditions

a novel lyapunov function for a non weighted l2 gain of asynchronously switched linear systems abstract in this paper a novel lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes the novelty consists in continuity of the lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched this structure is exploited to construct a time varying lyapunov function that is non increasing at time instants of discontinuity stability criteria based on the novel lyapunov function are developed to guarantee global asymptotic stability in the noiseless case most importantly when exogenous disturbances are considered the proposed lyapunov function can be used to guarantee a finite non weighted l 2 gain for asynchronously switched systems for which lyapunov functions proposed in literature are inconclusive a numerical example illustrates the effectiveness of the proposed method

an integral type multiple lyapunov functions approach for switched nonlinear systems an integral type multiple lyapunov functions mlfs approach for switched nonlinear systems is set up for the first time which gives a more general condition for analyzing the behavior of switched nonlinear systems since the branicky s nonincreasing condition is no longer assumed and the generalized mlfs condition is a special case of the condition provided meanwhile based on the integral type mlfs approach global stabilization for a class of switched nonlinear systems in p normal form is achieved by constructing state feedback controllers of subsystems and a proper switching law where the solvability of the problem under study for individual subsystems is not assumed two examples are also provided to demonstrate the effectiveness of the proposed design method

a fast recursive algorithm for the maximum likelihood estimation of the parameters of a periodic signal describes a new recursive algorithm for the estimation of the parameters of a periodic signal in additive gaussian white noise these parameters are the period and the complex amplitudes of the harmonics present the proposed algorithm is based on recursive maximum likelihood ml algorithms for incomplete data as described by titterington 1985 and others these algorithms are of complexity o nm where n is the number of harmonics and m is the signal length the performance of the method is compared to that of the extended kalman filter with the aid of simulations

a hybrid learning algorithm combined with generalized rls approach for radial basis function neural networks in this paper a new hybrid learning method for radial basis function neural networks based on generalized recursive least square algorithm is proposed firstly the generalized recursive least square grls model including a general quadratic weight decay term in the energy function for the training of rbf neural networks is described then combined with the grls approach a new hybrid learning method is proposed to meet the design goals improving the generalization ability of the trained network finally experimental results demonstrate that our approach can achieve a significantly improved generalization performance of the rbf networks

comparative study of four adaptive frequency trackers we study and compare four algorithms for adaptive retrieval of slowly time varying multiple cisoids in noise the adaptive notch filter the multiple frequency tracker the adaptive estimation scheme and the hyperstable adaptive line enhancer the local behavior of the algorithms in a neighborhood of their equilibrium state assuming high signal to noise ratio snr and large data sample for a two cisoid signal is treated in a similar way to the linear filter approximation technique used for a single cisoid case the validity of the results is confirmed by computer simulations

adaptive polynomial factorization by coefficient matching a polynomial factorization algorithm is presented which updates all roots simultaneously and efficiently in response to coefficient perturbations the algorithm requires approximately 2n sup 2 complex floating point operations to update all roots of nth order polynomial close to the true root vector the algorithm s convergence rate is quadratic the root update requires only the solution of two sets of structured linear equations and a convolution the algorithm can be used to track the roots of time varying polynomials which is useful for application in adaptive signal processing

infinite propagation speed of the camassa holm equation we use the inverse scattering transform to show that a solution of the camassa holm equation is identically zero whenever it vanishes on two horizontal half lines in the x t space in particular a solution that has compact support at two different times vanishes everywhere proving that the camassa holm equation has infinite propagation speed

adaptive algorithms for constrained arma signals in the presence of noise a family of algorithms is developed for adaptive parameter estimation of constrained autoregressive moving average arma signals in the presence of noise these algorithms utilize a priori information about the signal s properties such as its spectral type for example low pass bandpass etc or a spatial domain characteristic special applications include modeling of autoregressions ar and signals of known spectral type in the presence of noise signal deconvolution image deblurring and multipath parameter estimation selected results of simulations are included to demonstrate the performance of the algorithms

analysis of state space system identification methods based on instrumental variables and subspace fitting subspace based state space system identification 4sid methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification the advantages are that the user has simple and few design variables and that the methods have robust numerical properties and relatively low computational complexities though subspace techniques have been demonstrated to perform well in a number of cases the performance of these methods is neither fully understood nor analyzed our principal objective is to undertake a statistical investigation of subspace based system identification techniques the studied methods consist of two steps the subspace spanned by the extended observability matrix is first estimated the asymptotic properties of this subspace estimate are derived herein in the second step the structure of the extended observability matrix is used to find a system model estimate two possible methods are considered the simplest one only uses a certain shift invariance property while in the other method a parametric representation of the null space of the observability matrix is exploited explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given

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

nonfragile h_ infty fuzzy filtering with randomly occurring gain variations and channel fadings this paper is concerned with the nonfragile h infty filtering problem for a class of discrete time takagi sugeno t s fuzzy systems with both randomly occurring gain variations rogvs and channel fadings the phenomenon of the rogvs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation two sequences of random variables obeying the bernoulli distribution are employed to describe the phenomenon of the rogvs bounded by prescribed norms in addition the rice fading model is utilized to describe the phenomena of channel fadings where the occurrence probabilities of the random channel coefficients are allowed to time varying through stochastic analysis and lyapunov functional approach sufficient conditions are established under which the filtering error dynamics is exponentially mean square stable with a prespecified h infty performance the set of the desired nonfragile h infty filters is characterized by solving a convex optimization problem via the semidefinite programming method an illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper

on solutions of the camassa holm equation the techniques that have been developed for the application of the inverse scattering transform method to the solution of the camassa holm equation principally by constantin are implemented we use this approach first to represent the known solitary wave solution in a simple parametric form and then second to obtain the general two and three soliton solutions these latter two solutions require rather extensive use of mathematical packages mathematica and maple in order to complete the construction of solutions a number of examples are presented the phase shifts evident after an interaction are found and the special limit that recovers the peakon solutions is discussed

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

non weighted quasi time dependent h filtering for switched linear systems with persistent dwell time this paper is concerned with h filtering for a class of switched linear systems in discrete time domain a more general class of switching signals the persistent dwell time pdt switching is considered rather than the dwell time or average dwell time switching often studied in the literature the concept on a stage of switching in the type of pdt switching signals is introduced and each stage consists of a period of persistence and a dwell time portion in which no switching occurs a proper lyapunov function suitable to the pdt switching is constructed which is not only mode dependent but also quasi time dependent qtd then a qtd filter is designed such that the resulting filtering error system is globally uniformly asymptotically stable and has a guaranteed h noise attenuation performance certain techniques are explored such that the obtained performance index is of strictly non weighted h norm which contrasts with the weighted or called exponential ones i e weaker noise attenuation in the existing literature of switched systems with average dwell time an example of mass spring system is provided to show the validity and potential of the developed results

adaptive parameter estimation for a constrained low pass system a novel algorithm is presented for adaptive parameter estimation for a constrained low pass butterworth system model the algorithm will estimate the system cutoff frequency and gain online when it is known that the true system has a low pass butterworth structure or some transfer function similar to it and its true order is used the algorithm will lead to a substantial savings in computation and more accurate results than unconstrained algorithms potential applications include filter design and adaptive decision on nyquist rate for systems

on the computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

adaptive pole estimation an adaptive algorithm is developed for online estimation of the poles of autoregressive ar processes the method estimates the poles directly from the data without intermediate estimation of the ar coefficients or polynomial factorization it converges rapidly is computationally efficient and attains the cramer rao bound crb asymptotically a closed form expression for the asymptotic crb is provided convergence to the true solution is proved and methods are discussed for extending the algorithm for use with more general e g autoregressive moving average models numerical examples are presented to demonstrate the performance of the algorithm

periodic signal analysis by maximum likelihood modeling of orbits of nonlinear odes this paper treats a new approach to the problem of periodic signal estimation the idea is to model the periodic signal as a function of the state of a second order nonlinear ordinary differential equation ode this is motivated by poincare theory which is useful for proving the existence of periodic orbits for second order odes the functions of the right hand side of the nonlinear ode are then parameterized by a multivariate polynomial in the states where each term is multiplied by an unknown parameter a maximum likelihood algorithm is developed for estimation of the unknown parameters from the measured periodic signal the approach is analyzed by derivation and solution of a system of odes that describes the evolution of the cramer rao bound over time this allows the theoretically achievable accuracy of the proposed method to be assessed in the ideal case where the signals can be exactly described by the imposed model the proposed methodology reduces the number of estimated unknowns at least in cases where the actual signal generation resembles that of the imposed model this in turn is expected to result in an improved accuracy of the estimated parameters

a generalized constraint neural network model associating partially known relationships for nonlinear regressions in an attempt to enhance the neural network technique so that it can evolve from a black box tool into a semi analytical one we propose a novel modeling approach of imposing generalized constraints on a standard neural network we redefine approximation problems by use of a new formalization with the aim of embedding prior knowledge explicitly into the model to the maximum extent a generalized constraint neural network gcnn model has therefore been developed which basically consists of two submodels one is constructed by the standard neural network technique to approximate the unknown part of the target function the other is formed from partially known relationships to impose generalized constraints on the whole model three issues arising after combination of the two submodels are discussed a the better approximation provided by the gcnn model compared with a standard neural network b the identifiability of parameters in the partially known relationships and c the discrepancy in the approximation due to removable singularities in the target function numerical studies of three benchmark problems show important findings that have not previously been reported in the literature significant benefits were observed from using the gcnn model in comparison with a standard neural network

a delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

a sliding mode approach to stabilization of nonlinear markovian jump singularly perturbed systems this paper presents a sliding mode control smc method for a class of nonlinear markovian jump singularly perturbed systems mjspss the system is subject to parameter uncertainties and partly unknown transition probabilities to fully employ the model characteristics of such a hybrid system a novel integral type switching function is firstly designed by adopting the e dependent stochastic lyapunov function method sufficient conditions are presented to ensure the mean square asymptotic stability of the sliding mode dynamics a mode dependent fuzzy smc law is then synthesized to induce and maintain the sliding motion despite partly unknown transition probabilities and parameter uncertainties finally the developed method is applied to stabilize a modified series dc motor system

h_ infty filtering of discrete time switched systems with state delays via switched lyapunov function approach in this note the problem of hinfin filtering for a class of discrete time switched systems with state delays is investigated attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the hinfin sense by using switched lyapunov functionals sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities lmis by solving which a desired hinfin filter can be constructed a numerical example is provided to demonstrate the effectiveness of the proposed techniques

stationary points of the recursive generalized least squares algorithm for adaptive notch filtering possible convergence points of the generalized least squares adaptive notch filtering algorithm are analytically derived for the multiple sinusoid case showing explicitly the dependence of the asymptotic bias on the pole contraction factor signal to noise ratio and the true model parameters the results for symmetric and nonsymmetric parameterization are compared

asymptotic cramer rao bounds for estimation of the parameters of damped sine waves in noise the problem of estimating the parameters of a signal composed of several damped sine waves in noise has applications for example in transient signal analysis explicit closed form expressions are derived for the cramer rao bound of this problem in the case of low damping low spectral interference between the signal components and a sufficiently large number of samples among several conclusions which are drawn from the expressions it is found that the estimation problem is much more sensitive to errors in the damping factor and frequency than to errors in amplitude and phase

generalized adaptive comb filters smoothers and their application to the identification of quasi periodically varying systems and signals the problem of both causal and noncausal identification of linear stochastic systems with quasi harmonically varying parameters is considered the quasi harmonic description allows one to model nonsinusoidal quasi periodic parameter changes the proposed identification algorithms are called generalized adaptive comb filters smoothers because in the special signal case they reduce down to adaptive comb algorithms used to enhance or suppress nonstationary harmonic signals embedded in noise the paper presents a thorough statistical analysis of generalized adaptive comb algorithms and demonstrates their statistical efficiency in the case where the fundamental frequency of parameter changes varies slowly with time according to the integrated random walk model

metrics for vector quantization based parametric speech enhancement and separation speech enhancement and separation algorithms sometimes employ a two stage processing scheme wherein the signal is first mapped to an intermediate low dimensional parametric description after which the parameters are mapped to vectors in codebooks trained on for example individual noise free sources using a vector quantizer to obtain accurate parameters one must employ a good estimator in finding the parameters of the intermediate representation like a maximum likelihood estimator this leaves some unanswered questions however like what metrics to use in the subsequent vector quantization process and how to systematically derive them this paper aims at answering these questions metrics for this are presented and derived and their use is exemplified on a number of different signal models by deriving closed form expressions the metrics essentially take into account in the vector quantization process that some parameters may have been estimated more accurately than others and that there may be dependencies between the estimation errors

observer based control for piecewise affine systems with both input and output quantization this technical note is concerned with the problem of simultaneous design of observers and controllers for a class of piecewise affine systems against signal quantization occurring in both measurement output and control input channels the general scenario is considered that system state and estimated state may not be in the same operating region by a novel quantization error dependent lyapunov function the stability and mathcal h infty performance criteria are first established for the augmented system composed of a closed loop control system and an estimation error system with the aid of s procedure involving the region partition information of the original system then by the cone complementary linearization algorithm the desired observer and controller gains are solved simultaneously such that the resulting closed loop system is asymptotically stable with a prescribed mathcal h infty performance index finally a networked single link robot arm is utilized to demonstrate the effectiveness of the proposed control strategy

a stability condition for certain bilinear systems the authors derive a simple sufficient condition for the output of a discrete time time invariant bilinear system to be bounded whenever the input signal to the system is bounded by a finite constant

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

on the geometric approach to the motion of inertial mechanical systems according to the principle of least action the spatially periodic motions of one dimensional mechanical systems with no external forces are described in the lagrangian formalism by geodesics on a manifold configuration space the group d of smooth orientation preserving diffeomorphisms of the circle the periodic inviscid burgers equation is the geodesic equation on d with the l 2 right invariant metric however the exponential map for this right invariant metric is not a c 1 local diffeomorphism and the geometric structure is therefore deficient on the other hand the geodesic equation on d for the h 1 rightinvariant metric is also a re expression of a model in mathematical physics we show that in this case the exponential map is a c 1 local diffeomorphism and that if two diffeomorphisms are sufficiently close on d t heycan be joined by a unique length minimizing geodesic a state of the system is transformed to another nearby state by going through a uniquely determined flow that minimizes the energy we also analyse for both metrics the breakdown of the geodesic flow

zeroing polynomials using modified constrained neural network approach this paper proposes new modified constrained learning neural root finders nrfs of polynomial constructed by backpropagation network bpn the technique is based on the relationships between the roots and the coefficients of polynomial as well as between the root moments and the coefficients of the polynomial we investigated different resulting constrained learning algorithms clas based on the variants of the error cost functions ecfs in the constrained bpn and derived a new modified cla mcla and found that the computational complexities of the cla and the mcla based on the root moment method rmm are the order of polynomial and that the mcla is simpler than the cla further we also discussed the effects of the different parameters with the cla and the mcla on the nrfs in particular considering the coefficients of the polynomials involved in practice to possibly be perturbed by noisy sources thus we also evaluated and discussed the effects of noises on the two nrfs finally to demonstrate the advantage of our neural approaches over the nonneural ones a series of simulating experiments are conducted

a robust spectral estimation by modeling an estimated autocovariance with an arma model the development analysis simulation results and comparison of techniques for estimating spectral peaks of stationary signals in environments with low signal to noise ratio are discussed unlike traditional parametric methods the proposed method estimates parameters of a model which best approximates the estimated autocovariance lag rather than the received signal this technique is studied and evaluated in three different respects using a performance index in the spectral domain suppression of the moving average ma portion and in terms of effective signal to noise ratio this estimation technique demonstrates outstanding robustness and resolution for estimating both spectral peaks and amplitudes of multiple sinusoids embedded in white gaussian noise compared to traditional methods when used in conjunction with cadzow s autoregressive moving average arma method using singular value decomposition svd the technique extracts frequencies and amplitudes of existing sinusoids down to 17 db while the arma method alone achieves only 10 db on average

a constructive approach for finding arbitrary roots of polynomials by neural networks this paper proposes a constructive approach for finding arbitrary real or complex roots of arbitrary real or complex polynomials by multilayer perceptron network mlpn using constrained learning algorithm cla which encodes the a priori information of constraint relations between root moments and coefficients of a polynomial into the usual bp algorithm bpa moreover the root moment method rmm is also simplified into a recursive version so that the computational complexity can be further decreased which leads the roots of those higher order polynomials to be readily found in addition an adaptive learning parameter with the cla is also proposed in this paper an initial weight selection method is also given finally several experimental results show that our proposed neural connectionism approaches with respect to the nonneural ones are more efficient and feasible in finding the arbitrary roots of arbitrary polynomials

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed methods

a new partitioning neural network model for recursively finding arbitrary roots of higher order arbitrary polynomials a new partitioning feedforward neural network fnn root finder model for recursively finding the arbitrary including complex roots of higher order arbitrary polynomials is proposed in this paper moreover an efficient complex version of constrained learning algorithm cla which incorporates the a priori information i e the constrained relation between the original polynomial coefficients and the remaining polynomial coefficients plus the partitioned roots out from the original polynomial is constructed to train the corresponding partitioning neural root finder network for finding the arbitrary roots of arbitrary polynomials finally the experimental results are given to show the efficiency and effectiveness of our proposed neural model with respect to traditional non neural root finders

ramanujan sums in the context of signal processing part ii fir representations and applications the mathematician ramanujan introduced a summation in 1918 now known as the ramanujan sum c q n in a companion paper part i properties of ramanujan sums were reviewed and ramanujan subspaces s q introduced of which the ramanujan sum is a member in this paper the problem of representing finite duration fir signals based on ramanujan sums and spaces is considered first it is shown that the traditional way to solve for the expansion coefficients in the ramanujan sum expansion does not work in the fir case two solutions are then developed the first one is based on a linear combination of the first n ramanujan sums with n being the length of the signal the second solution is based on ramanujan subspaces with q 1 q 2 q k denoting the divisors of n it is shown that x n can be written as a sum of k signals x qi n s qi furthermore the i th signal x qi n has period q i and any pair of these periodic components is orthogonal the components x qi n can be calculated as orthogonal projections of x n onto ramanujan spaces s qi then the ramanujan periodic transform rpt is defined based on this and is useful to identify hidden periodicities it is shown that the projection matrices which compute x qi n from x n are integer matrices except for an overall scale factor the calculation of projections is therefore rendered easy to estimate internal periods n n of x n one only needs to know which projection energies are nonzero

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

an iterative method for exact maximum likelihood estimation of the parameters of a harmonic series a procedure is described for determining the exact maximum likelihood ml estimates of the parameters of a harmonic series i e the fundamental frequency and the amplitude and phase of each harmonic existing ml methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored these terms asymptotically reduce to zero as the sample size increases to infinity it is argued that these terms can be significant for short signal lengths the application of the expectation maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface if global convergence results this point yields the exact ml estimates simulation studies illustrate the advantages of the method when short data lengths are used

finding the zeros of linear phase fir frequency sampling digital filters the need for finding the zeros of fir filters often arises in digital signal processing applications if we want to convert linear phase finite impulse response fir filters into minimum phase fir filters 1 2 the problem of finding the zeros of the filter is encountered this problem has been addressed in 3 but not solved here we introduce the idea of using frequency sampling filters for obtaining its zeros the advantage of using this kind of filter resides in the fact that all the zeros on the unit circle are known furthermore the zeros off the unit circle can be obtained with some simple processing this type of filter is especially useful when high order narrow band filters are involved finding the zeros of very high order equirriple low pass filters can be a difficult if not impossible task

finite propagation speed for the camassa holm equation we prove that any classical solution of the camassa holm equation will have compact support if its initial data has this property

filtering for discrete time switched fuzzy systems with quantization the paper is concerned with the h infty and l 2 l infty filtering design problems for discrete time nonlinear switched systems with quantized measurements using the takagi sugeno t s fuzzy model the systems under consideration inherently combine features of the switched hybrid systems and the t s fuzzy systems the sector bound approach is employed to deal with quantization effects based on the fuzzy basis dependent lyapunov function sufficient conditions are established such that the filtering error system is stochastically stable and a prescribed noise attenuation level in an h infty or l 2 l infty sense is achieved both numerical and practical examples are provided to show the feasibility and efficiency of the design schemes

periodic signal modeling based on lie spl acute nard s equation the problem of modeling periodic signals is considered the approach taken here is motivated by the well known theoretical results on the existence of periodic orbits for lie spl acute nard systems and previous results on modeling periodic signals by means of second order nonlinear ordinary differential equations the approach makes use of the appropriate conditions imposed on the polynomials of the lie spl acute nard s system to guarantee the existence of a unique and stable limit cycle these conditions reduce the number of parameters required to generate accurate models

nonfragile quantized h filtering for discrete time switched t s fuzzy systems with local nonlinear models this paper addresses the h infty filtering problem for a class of discrete time nonlinear switched systems every subsystem of the considered nonlinear switched systems is represented by the takagi sugeno t s fuzzy systems with local nonlinear models signal quantization and filter parameter perturbation are considered simultaneously in the h infty filter design both the measurement output signal and the performance output signal are quantized by two static quantizers respectively before they are transmitted based on the average dwell time approach sufficient conditions for desired h infty filters are established in the form of linear matrix inequalities lmis under the obtained conditions the filtering error system is exponentially stable and can achieve a weighted h infty performance index finally a numerical example and a practical example are provided to illustrate the effectiveness of the obtained results

a new approach for function approximation incorporating adaptive particle swarm optimization and a priori information in this paper a new approach coupling adaptive particle swarm optimization apso and a priori information for function approximation problem is proposed to obtain better generalization performance and faster convergence rate it is well known that gradient based learning algorithms such as backpropagation bp algorithm have good ability of local search whereas pso has good ability of global search therefore in the new approach first apso encoding the first order derivative information of the approximated function is applied to train network to near global minima second with the connection weights produced by apso the network is trained with a gradient based algorithm due to combining apso with local search algorithm and considering a priori information the new approach has better generalization performance and convergence rate than traditional learning ones finally simulation results are given to verify the efficiency and effectiveness of the proposed approach

polynomial fuzzy model based control systems stability analysis via approximated membership functions considering sector nonlinearity of control input this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions in order to address the input nonlinearity the control signal is considered to be bounded by a sector with nonlinear bounds these nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account with the consideration of imperfectly matched membership functions and input nonlinearity the applicability of the pfmb control scheme can be further enhanced to facilitate the stability analysis a general form of approximated membership functions representing the original ones is introduced as a result approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions the sum of squares approach is employed to obtain the stability conditions based on lyapunov stability theory simulation examples are presented to demonstrate the feasibility of the proposed method

all pole estimation in spectral domain autoregressive ar modeling is a popular spectral analysis method commonly resolved in the time domain this paper presents a novel ar analysis framework dealing with the estimation of poles directly from spectral samples the basis of the method lies on a minimizing functional built with a certain mapping of the spectral residue the optimization mechanism is based on the multivariate newton raphson algorithm two different mappings are considered namely linear and logarithmic the linear case results in a nonquadratic convex functional whose global minimum is equivalent to that of the time domain autocorrelation method the logarithmic case under the maximum likelihood criterion turns out equivalent to the whittle likelihood proven here to be suitable for frequency selective estimation the statistical and convergence performance of the method is demonstrated with simulations on stochastic and deterministic harmonic signals

fault detection filtering for nonlinear switched stochastic systems in this note the fault detection filtering problem is solved for nonlinear switched stochastic system in the t s fuzzy framework our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with brownian motion based on observer based fault detection fuzzy filter as a residual generator the proposed fault detection is formulated as a fuzzy filtering problem by the utilization of the average dwell time technique and the piecewise lyapunov function technique the fuzzy parameter dependent fault detection filters are designed that guarantee the resulted error system to be mean square exponential stable with a weighted mathcal h infty error performance then the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique finally simulation has been presented to show the effectiveness of the proposed fault detection technique

on the accuracy of the kumaresan tufts method for estimating complex damped exponentials recently kumaresan and tufts kt presented a method for estimating the parameters of damped exponential waveforms in additive white noise the kt method uses singular value decomposition svd of the data matrix with truncation and backward prediction to improve the accuracy of the estimates the kt method was demonstrated to have a very good performance in comparison to traditional methods used for the same problem e g prony s method kumaresan and tufts also showed by numerical simulations that the variances of the estimates obtained by their method approaches the cramer rao lower bounds for selected test cases in this correspondence we provide a quantitative accuracy analysis of the kt method the analysis is based on first order taylor series approximations of the estimated parameters around their true values no assumptions are made on the number of data points used but it is assumed that the noise level is small enough for the first order approximations to be valid results of the analysis are illustrated by some numerical examples these results confirm the good performance of the kt method and show the effect of the user chosen parameters on the accuracy of the estimates

generalized adaptive notch and comb filters for identification of quasi periodically varying systems the problem of identification tracking of quasi periodically varying real valued systems is considered this problem is a generalization to the system case of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise the solution is based on the exponentially weighted basis function ewbf approach the proposed algorithms are capable of tracking slow changes in system frequencies which means that not only the expansion coefficients in the basis function description of the analyzed system but also the basis functions themselves are adjusted in an adaptive manner first assuming that the system frequencies are known and constant the running basis and fixed basis variants of the ewbf algorithm are derived and their relationship to the classical notch filter with constrained poles and zeros is established next the frequency adaptive versions of both algorithms are obtained using the gradient search and recursive prediction error principles respectively finally the interrelated frequencies case is analyzed and two additional parameter tracking algorithms generalized adaptive comb filters are derived

tracking analysis of an adaptive notch filter with constrained poles and zeros this paper analyzes the asymptotic tracking properties of an adaptive notch filter anf with pole zero constraints for the cancellation or retrieval of multiple time varying sine waves in additive noise the asymptotic mean square error mse is analyzed using the methods of ljung and gunnarsson 1990 when the variations in the underlying frequencies are assumed to be sufficiently small closed form expressions for the mse are derived as functions of the tuning variables of the algorithm the results give insight into the operational properties of the algorithm and are used in order to minimize the mse with respect to the tuning variables computer simulations confirm the validity of the derived results