a geometrical fuzzy clustering based solution to glottal wave estimation accurate estimation of the glottal waveform gw is required for purposes such as natural speech synthesis speaker recognition physiological speech processing etc most methods available for gw estimation are based on inverse filtering of the speech signal through the vocal tract and they all suffer from inaccuracies due to incorrect assumptions the method for gw estimation developed in the present study is based on fuzzy clustering of quasi linear geometrical substructures represented within the signal shifts hyperspace algorithms for estimation of the driving function to the vocal tract are presented and evaluated on simulated and real data comparison of the fuzzy clustering based method with the psiaif and wong s closed phase algorithms shows that the present method is superior with respect to both the gw estimation and determination of gw event time instants

a harmonic retrieval framework for discontinuous motion estimation motion discontinuities arise when there are occlusions or multiple moving objects in the scene that is imaged conventional regularization techniques use smoothness constraints but are not applicable to motion discontinuities in this paper we show that discontinuous or multiple motion estimation can be viewed as a multicomponent harmonic retrieval problem from this viewpoint a number of established techniques for harmonic retrieval ran be applied to solve the challenging problem of discontinuous or multiple motion compared with existing techniques the resulting algorithm is not iterative which not only implies computational efficiency but also obviates concerns regarding convergence or local minima it also adds flexibility to spatio temporal techniques which have suffered from lack of explicit modeling of discontinuous motion experimental verification of our framework on both synthetic data as well as real image data is provided

parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

motion estimation in the frequency domain using fuzzy c planes clustering a previous work explicitly models the discontinuous motion estimation problem in the frequency domain where the motion parameters are estimated using a harmonic retrieval approach the vertical and horizontal components of the motion are independently estimated from the locations of the peaks of respective periodogram analyses and they are paired to obtain the motion vectors using a procedure proposed by chen giannakis nandhakumar see ieee trans image processing vol 7 p 1242 56 1998 in this paper we present a more efficient method that replaces the motion component pairing task and hence eliminates the problems of the pairing method described by chen et al the method described in this paper uses the fuzzy c planes fcp clustering approach to fit planes to three dimensional 3 d frequency domain data obtained from the peaks of the periodograms experimental results are provided to demonstrate the effectiveness of the proposed method

adaptive finite time bipartite consensus for second order multi agent systems with antagonistic interactions abstract this paper is concerned with the adaptive finite time bipartite consensus problems for networked second order multi agent systems with antagonistic interactions and unknown external disturbances a signed undirected graph is used to describe the interactions among agents for the leaderless case continuous nonlinear distributed protocols with adaptive update laws are given which can not only guarantee the bipartite steady state errors of any two agents converge to a small region in finite time but also eliminate the chattering problem then the proposed algorithm is extended to solve the adaptive finite time bipartite consensus tracking problem for leader follower case by designing distributed finite time estimator simulation example is included to show the effectiveness of the presented methods

technical communique identification of dynamical systems with a robust interval fuzzy model in this paper we present a new method of interval fuzzy model identification the method combines a fuzzy identification methodology with some ideas from linear programming theory on a finite set of measured data an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used the idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values this results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters the model is called the interval fuzzy model infumo the method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed we believe that the fuzzy interval model can be very efficiently used especially in fault detection and in robust control design

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

fuzzy shell clustering algorithms in image processing fuzzy c rectangular and 2 rectangular shells objective function based clustering has been generalized recently to detect contours of circles and ellipses or even hyperbolas in a set of binary data vectors although there are special algorithms to discover lines the detection of rectangles needs further treatment a simple line detection algorithm is not sufficient for rectangles since for identifying four lines as one rectangle additional information such as the length of the lines and whether they are parallel or meet at a right angle is necessary in this paper a special fuzzy shell clustering algorithm for rectangular contours is developed the principal idea behind it can be generalized for other polygons so we also derive an algorithm that is capable of detecting rectangles and other polygons as well as approximating circles ellipses and lines

a nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems a new infinitesimal sufficient condition is given for uniform global asymptotic stability ugas for time varying nonlinear systems it is used to show that a certain relaxed persistency of excitation condition called uniform spl delta persistency of excitation u spl delta pe is sufficient for uniform global asymptotic stability in certain situations u spl delta pe of the right hand side of a time varying differential equation is also shown to be necessary under a uniform lipschitz condition the infinitesimal sufficient condition for ugas involves the inner products of the flow field with the gradients of a finite number of possibly sign indefinite locally lipschitz lyapunov like functions these inner products are supposed to be bounded by functions that have a certain nested or triangular negative semidefinite structure this idea is reminiscent of a previous idea of matrosov who supplemented a lyapunov function having a negative semidefinite derivative with an additional function having a derivative that is definitely nonzero where the derivative of the lyapunov function is zero for this reason we call the main result a nested matrosov theorem the utility of our results on stability analysis is illustrated through the well known case study of the nonholonomic integrator

wide sense stationary processes forming frames in this paper we study the question of the representation of random variables by means of frames or riesz basis generated by stationary sequences this concerns the representation of continuous time wide sense stationary random processes by means of discrete samples

comments on discrete chirp fourier transform and its application to chirp rate estimation with reply this comment points out that the sample rate of the discrete chirp fourier transform dcft proposed by xia see ibid vol 48 p 3122 33 2000 is not sufficient to avoid severe picket fence effect and causes some restrictions for its practical applications by increasing the sample rate and modifying the dcft definition a new robust dcft is proposed xia see ibid vol 50 no 12 p 3116 2002 replies by first correcting an error on the analog to discrete parameter conversions of a chirp signal xia also add that when the chirp rate detection resolution is increased it is more robust to the chirp rate error on the other hand what is sacrificed by doing so is that the magnitudes of the sidelobes of the transform are increased which may limit its capability of detecting chirps in a multicomponent or low snr signal therefore which dcft needs to be used has to depend on the practical application

a consensus algorithm in cat 0 space and its application to distributed fusion of phylogenetic trees abstract based on convex analysis a novel consensus algorithm of dynamical points in a cat 0 space is developed in this paper in which the associated communication graph uniformly contains a directed spanning tree the proposed algorithm provides an efficient method of solving consensus problems in a general cat 0 space while having certain robustness against weak communication the application of the new algorithm to the distributed fusion of phylogenetic trees is shown with demonstrative case simulations together with a study on the algorithm s robustness and efficiency

frame sequences and representations for samplable random processes abstract in this work we characterize random processes which can be linearly determined using a frame sequence of random variables in particular these could be the discrete samples of a continuous time process we study the stable representation of continuous time processes by means of discrete samples or measurements of the original process finally we study how these representations can be applied to reduce the effects of reconstructing a random signal from samples corrupted by additive noise

a parametric model for fusing heterogeneous fuzzy data presented is a model that integrates three data types numbers intervals and linguistic assessments data of these three types come from a variety of sensors one objective of sensor fusion models is to provide a common framework for data integration processing and interpretation that is what our model does we use a small set of artificial data to illustrate how problems as diverse as feature analysis clustering cluster validity and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model the effects of reparameterization on computational outputs are discussed numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types

finite time connectivity preserving consensus of networked nonlinear agents with unknown lipschitz terms this technical note studies finite time consensus problem for a team of networked nonlinear agents with unknown lipschitz terms under communication constraints where each agent has a limited sensing range because the induced interaction graph is typically state dependent and dynamic we propose a distributed nonlinear consensus algorithm that is capable of preserving the initial interaction patterns by using tools from nonsmooth analysis sufficient conditions are obtained such that finite time consensus can be reached an upper bound of the convergence time is derived via a two step analysis the validity of the theoretical result is shown by one simulation example

estimation of multiple 2 d uniform motions by slide subspace based line detection a technique is proposed for estimating the parameters of two dimensional 2 d uniform motion of multiple moving objects in a scene based on long sequence image processing and the application of a multiline fitting algorithm plots of the vertical and horizontal projections versus frame number give new images in which uniformly moving objects are represented by skewed band regions with the angles of the skew from the vertical being a measure of the velocities of the moving objects for example vertical bands will correspond to objects with zero velocity an algorithm called subspace based line detection slide can be used to efficiently determine the skew angles slide exploits the temporal coherence between the contributions of each of the moving patterns in the frame projections to enhance and distinguish a signal subspace that is defined by the desired motion parameters a similar procedure can be used to determine the vertical velocities some further steps must then be taken to properly associate the horizontal and vertical velocities

estimation of motions in color image sequences using hypercomplex fourier transforms although the motion estimation problem has been extensively studied most of the proposed estimation approaches deal mainly with monochrome videos the most usual way to apply them also in color image sequences is to process each color channel separately a different more sophisticated approach is to process the color channels in a ldquoholisticrdquo manner using quaternions as proposed by ell and sangwine in this paper we extend standard spatiotemporal fourier based approaches to handle color image sequences using the hypercomplex fourier transform we show that translational motions are manifested as energy concentration along planes in the hypercomplex 3d fourier domain and we describe a methodology to estimate the motions based on this property furthermore we compare the three channels separately approach with our approach and we show that the computational effort can be reduced by a factor of 1 3 using the hypercomplex fourier transform also we propose a simple accompanying method to extract the moving objects in the hypercomplex fourier domain our experimental results on synthetic and natural images verify our arguments throughout the paper

a frequency domain algorithm for multiframe detection and estimation of dim targets an algorithm for detecting moving targets by imaging sensors and estimating their trajectories is proposed the algorithm is based on directional filtering in the frequency domain using a bank of filters for all possible target directions the directional filtering effectively integrates the target signal resulting in an improved signal to noise ratio working in the frequency domain facilitates a considerable reduction in computational requirements compared to time domain algorithms the algorithm is described in detail and its false alarm and detection probabilities are analyzed

a new variational approach for restoring images with multiplicative noise this paper proposes a novel variational model for restoration of images corrupted with multiplicative noise it combines a fractional order total variational filter with a high order pde laplacian norm the combined approach is able to preserve edges while avoiding the blocky effect in smooth regions this strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori map semi implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional to improve the numerical results we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial and error method the existence and uniqueness of a solution to the proposed variational model is established in this study parameter dependence is also discussed experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding pde methods

detection and separation of ring shaped clusters using fuzzy clustering a new fuzzy clustering algorithm designed to detect and characterize ring shaped clusters and combinations of ring shaped and compact spherical clusters has been developed this fkr algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric intersected combinations of clusters validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set the fkr algorithm has been tested on a variety of simulated combinations of ring shaped and compact spherical clusters and its performance proved to be very good both in identifying the input shapes and in recovering the input parameters application of the fkr algorithm to an mri image of the heart s left ventricle was used to investigate the possibility of using this algorithm as an aid in image processing

discrete chirp fourier transform and its application to chirp rate estimation the discrete fourier transform dft has found tremendous applications in almost all fields mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics in many applications wideband and nonstationary signals however often occur one of the typical examples of such signals is chirp type signals that are usually encountered in radar signal processing such as synthetic aperture radar sar and inverse sar imaging due to the motion of a target the radar return signals are usually chirps and their chirp rates include the information about the target such as the location and the velocity in this paper we study discrete chirp fourier transform dcft which is analogous to the dft besides the multiple frequency matching similar to the dft the dcft can be used to match the multiple chirp rates in a chirp type signal with multiple chirp components we show that when the signal length n is prime the magnitudes of all the sidelobes of the dcft of a quadratic chirp signal are 1 whereas the magnitude of the mainlobe of the dcft is spl radic n with this result an upper bound for the number of the detectable chirp components using the dcft is provided in terms of signal length and signal and noise powers we also show that the n point dcft performs optimally when n is a prime

orthogonal sampling formulas a unified approach this paper intends to serve as an educational introduction to sampling theory basically sampling theory deals with the reconstruction of functions signals through their values samples on an appropriate sequence of points by means of sampling expansions involving these values in order to obtain such sampling expansions in a unified way we propose an inductive procedure leading to various orthogonal formulas this procedure which we illustrate with a number of examples closely parallels the theory of orthonormal bases in a hilbert space all intermediate steps will be described in detail so that the presentation is self contained the required mathematical background is a basic knowledge of hilbert space theory finally despite the introductory level some hints are given on more advanced problems in sampling theory which we motivate through the examples

a clustering algorithm for fuzzy model identification the fuzzy model proposed by takagi and sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules in this paper the model is firstly modified to make its identification easier based on the fuzzy c partition space four criteria are proposed for optimization of the model parameters following that a clustering algorithm composed of fuzzy c linear functions clustering and like fuzzy c means clustering is developed for minimizing the four criteria an identification scheme for rule s premise and consequence parameters is deduced from the clustering algorithm in succession finally four examples are demonstrated to verify the effectiveness of the proposed algorithm

relational generalizations of cluster validity indices numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another one such scheme clustering looks for self similar groups of objects to use clustering algorithms an investigator must often have a priori knowledge of the number of clusters i e c to search for in the data moreover it is often convenient to have ways to rank the returned results either for a single value of c a range of c s different clustering methods or any combination thereof however the task of assessing the quality of the results so that c may be determined objectively is currently ill defined for object object relationships to bridge this gap we generalize three well known validity indices the modified hubert s gamma xie beni and the generalized dunn s indices to relational data in doing so we develop a framework to convert many other validity indices to a relational form numerical examples on 12 datasets samples from four normal mixtures four real world object datasets and four real world pure relational datasets using the relational duals of the hard fuzzy and possibilistic c means cluster algorithms are offered to illustrate and evaluate the new indices

linear fuzzy clustering techniques with missing values and their application to local principal component analysis in this paper we propose two methods for partitioning an incomplete data set with missing values into several linear fuzzy clusters by extracting local principal components one is an extension of fuzzy c varieties clustering that can be regarded as the algorithm for the local principal component analysis of fuzzy covariance matrices the other is a simultaneous application of fuzzy clustering and principal component analysis of fuzzy correlation matrices both methods estimate prototypes ignoring only missing values and they need no preprocessing of data such as the elimination of samples with missing values or the imputation of missing elements numerical examples show that the methods provide useful tools for interpretation of the local structures of a database

estimation of multiple time varying motions using time frequency representations and moving objects segmentation we extend existing spatiotemporal approaches to handle time varying motions estimation of multiple objects it is shown that multiple time varying motions estimation is equivalent to the instantaneous frequency estimation of superpoliteness fm sinusoids therefore we apply established signal processing tools such as time frequency representations to show that for each time instant the energy is concentrated along planes in the 3 d space spatial frequencies instantaneous frequency using fuzzy c planes we estimate indirectly the instantaneous velocities furthermore adapting existing approaches to our problem we attain the identification of the moving objects the experimental results verify the effectiveness of our methodology

relational duals of cluster validity functions for the c means family clustering aims to identify groups of similar objects to evaluate the results of cluster algorithms an investigator uses cluster validity indices while the theory of cluster validity is well established for vector object data little effort has been made to extend it to relationship based data as such this paper proposes a theory of reformulation for object data validity indices so that they can be used to rank the results produced by the relational means clustering algorithms more specifically we create a class of relational validity indices which is called dual relational indices that are guaranteed under certain but easily met constraints to produce the same results and hence the same cluster counts as their object data counterparts

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

frequency domain analysis of translations with piecewise cubic trajectories translations with piecewise cubic trajectories are studied in the frequency domain this class of motion has as an important subcase cubic spline trajectories translations with trajectories depending on time with general polynomial law are preliminarily considered and a general theorem concerning this type of motion is introduced the application of this theorem to the case of cubic time dependence and the consideration of finite duration effects lead to the solution of the piecewise cubic trajectory case the results which are remarkably different from those concerning constant velocity translations clearly indicate the importance of the role of velocity and time duration in this respect they confirm the validity of constant velocity motion as a first order model for frequency domain analysis of motion

equivalence between representations for samplable stochastic processes and its relationship with riesz bases we characterize random signals which can be linearly determined by their samples this problem is related to the question of the representation of random variables by means of a countable riesz basis we study different representations for processes which are linearly determined by a countable riesz basis this concerns the representation of continuous time processes by means of discrete samples

local convergence of the fuzzy c means algorithms abstract much understanding has recently been gained concerning global convergence properties of the fuzzy c means fcm family of clustering algorithms these global convergence properties which hold for all iteration sequences guarantee that every fcm iteration sequence converges at least along a subsequence to a stationary point of an fcm objective function in this paper we prove a local convergence property that is a property pertaining to iteration sequences started near a solution specifically a simple result is proved which shows that whenever an fcm algorithm is started sufficiently near a minimizer of the corresponding objective function then the iteration sequence must converge to that particular minimizer the result guarantees that once captured by the local neighborhood of a minimizer the succeeding iterate sequence will not escape thus infinite oscillation of such a sequence cannot occur the rate of convergence of the sequence to such a point is also discussed

entropy encoding hilbert space and karhunen loeve transforms by introducing hilbert space and operators we show how probabilities approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates our main results yield orthogonal bases which optimize distinct measures of data encoding

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

a fuzzy based customer classification method for demand responsive logistical distribution operations in some cases customer classification is important for the development of advanced logistical distribution strategies in response to the growing complexity in business logistical markets this paper presents a new approach that can be employed to cluster customers before executing fleet routing in logistical operations the proposed approach is developed on the basis of fuzzy clustering techniques and involves three sequential mechanisms including 1 binary transformation 2 generation of a fuzzy correlation matrix and 3 customer clustering such a customer clustering method should be performed prior to vehicle dispatching and routing in the process of goods distribution the proposed methodology clusters customers on the basis of their demand attributes rather than the static geographic property which is considered extensively in most published vehicle routing algorithms in addition to methodology development a case study was conducted to demonstrate the potential advantages of the proposed fuzzy clustering based method it is expected that this study can stimulate more research on time based logistics control and management

two dimensional matched filtering for motion estimation in this work we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence the least squares optimum approach involves the computation of the three dimensional 3 d fourier transform of the sequence followed by the detection of one or more planes in this domain with high energy concentration we present a more efficient algorithm based on the properties of the radon transform and the two dimensional 2 d fast fourier transform which can sacrifice little performance for significant computational savings we accomplish the motion detection and estimation by designing appropriate matched filters the performance is demonstrated on two image sequences

spatiotemporal approach for time varying global image motion estimation image motion estimation using the spatiotemporal approach has largely relied on the constant velocity assumption and thus becomes inappropriate when the velocity of the imaged scene or the camera changes during the data acquisition time using a polynomial or a trigonometric polynomial model for the time variation of the image motion spatiotemporal algorithms are developed in this paper to handle time varying but space invariant motion under these models it is shown that time varying image motion estimation is equivalent to parameter estimation of one dimensional 1 d polynomial phase or phase modulated signals which allows one to exploit well established results in radar signal processing when compared with alternative approaches the resulting motion estimation algorithms produce more accurate estimates simulation results are provided to demonstrate the proposed schemes

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

recognition and velocity computation of large moving objects in images two one dimensional time sequences are generated from the projections of the two dimensional sequence on the x and y axes then the two dimensional fast fourier transform for the generated time sequences is computed a peak in the spectrum for the selected spatial frequency is detected the temporal frequency at which the peak is detected gives an estimate of the velocity of the moving object analytical formulations for large moving objects in a time sequence with zero background are presented an algorithm is given for velocity formulation

cooperative optimal control for lipschitz nonlinear systems over generally directed topologies abstract this paper studies the cooperative optimal control for multi agent systems mass with lipschitz nonlinearities over general digraphs the leader following consensus model consisting of multiple followers and one leader is constructed distributed optimal control protocols using the linear quadratic regulator approach are designed under the proposed protocols the performance index of the mas is optimized by solving the algebraic riccati equation are the weighting matrices of performance index rely on the lipschitz nonlinearities leading to optimal performance simulation studies are finally reported to illustrate the effectiveness of presented protocols

detection and characterization of cluster substructure ii fuzzy c varieties and convex combinations thereof in part i siam j appl math 40 1981 pp 339 357 fuzzy c lines was introduced as an algorithm for detection and characterization of linearly clustered data in part ii we address two extensions of the theory in part i specifically we will first generalize the straight line prototype of a cluster developed in part i to any r dimensional linear variety of r s 0 leqq r s secondly we will consider a distance functional which utilizes convex combinations of the distance functionals developed here and in part i all of the notation and symbols used here are unchanged from part i

estimation of time varying velocities of moving objects by time frequency representations an approach to the estimation of motion parameters of moving objects in a video sequence by using the slide subspace based line detection algorithm algorithm is considered the proposed procedure projects video frames to the coordinate axes in order to obtain synthetic images containing information about the motion parameters these synthetic images are mapped to the fm signals by using constant spl mu propagation the problem of velocity estimation is reduced to the instantaneous frequency if estimation if estimators based on time frequency tf representations are used three tf representations spectrogram spec wigner distribution wd and s method sm are used and compared to this aim a tradeoff between concentration of the tf representation velocity estimation accuracy and reduction of the cross terms possibility for estimation of the multiple objects parameters is achieved by the sm a performance analysis of the algorithm is done theoretical results are illustrated on several numerical examples

detection and characterization of cluster substructure i linear structure fuzzy c lines in part i a generalization of the fuzzy c means or fuzzy isodata clustering algorithms is developed necessary conditions for minimization of a generalized total weighted squared orthogonal error objective function lead to a picard iteration scheme which generates simultaneously i c fuzzy clusters in the data ii a set of c prototypical straight lines in feature space which best fit the data in a well defined sense iii a set of c prototpyical centers of mass on the c lines which characterize the core of each linear fuzzy cluster theoretical optimization is achieved using principal components of generalized within cluster fuzzy scatter matrices a convergence theorem for each algorithm in the infinite family is given the algorithms are exemplified by five numerical examples using both real and artificial data sets having essentially linear substructure in part ii the fuzzy c means and fuzzy c lines algorithms are shown to be special cases of a more general class of fuzzy algorithms the

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control