on robust hurwitz polynomials in this note kharitonov s theorem on robust hurwitz polynomials is simplified for low order polynomials specifically for n 3 4 and 5 the number of polynomials required to check robust stability is one two and three respectively instead of four furthermore it is shown that for n geq 6 the number of polynomials for robust stability checking is necessarily four thus further simplification is not possible the same simplifications arise in robust schur polynomials by using the bilinear transformation applications of these simplifications to two dimensional polynomials as well as to robustness for single parameters are indicated

necessary and sufficient conditions for robust stability of discrete systems with coefficients depending continuously on two interval parameters abstract let a real polynomial in a complex variable whose coefficients are any given continuous functions of two real interval parameters be given necessary and sufficient conditions are derived for the polynomial to have all its zeros outside or inside the unit circle of the complex variable plane in a multi polynomial dependence of the coefficients on parameters the conditions involve in addition to a finite number of algebraic steps only resolving single variable fixed coefficients real polynomials

a necessary and sufficient condition for schur invariance and generalized stability of polytopes of polynomials polytopes of characteristic polynomials arise when systems experience real parameter variations a necessary and sufficient condition requiring only a finite number of computations is presented for determining whether all the roots of a polytope of polynomials are contained in a desired region this can be any region that is the image of the open left half plane under a real linear fractional transformation since the open unit cycle is such a region this result establishes a finite algorithm for strict schur invariance finite algorithms for generalized stability regions such as maximum bandwidth and maximum setting time are also established

stability of polynomials under coefficient perturbation let the real polynomial a 0 x n a 1 x n 1 a n 1 x a n be stable and let the real numbers b k c k geq 0 0 leq k leq n be given we present a simple determinant criterion for finding the largest t 0 geq 0 such that the polynomial alpha 0 x n alpha 1 x n 1 alpha n 1 x alpha n is stable for all alpha k in a k b k t 0 a k c k t 0 cup a k 0 leq k leq n several further observations allow us to reduce the computational cost considerably

on compactness in bifuzzy topological spaces abstract compactness in a bifuzzy topological space has been studied earlier by abd el monsef and ramadan fuzzy sets and systems 30 1989 165 174 and safiya et al fuzzy sets and systems 62 1994 89 96 as generalizations of p compactness or s compactness in a bitopological space in section 2 of this note we have obtained some interesting results related to pc compactness introduced by safiya et al fuzzy sets and systems 62 1994 89 96 as a concept parallelling that of p compactness of bitopological spaces further in section 3 we have introduced and studied b compactness b compactness in a bifuzzy topological space which are parallel to the notion of b compactness in a bitopological space we have also defied b almost b almost compactness in a bfts which is weaker than b compactness b compactness several related results have been proved

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

robust algebraic segmentation of mixed rigid body and planar motions from two views this paper studies segmentation of multiple rigid body motions in a 3 d dynamic scene under perspective camera projection we consider dynamic scenes that contain both 3 d rigid body structures and 2 d planar structures based on the well known epipolar and homography constraints between two views we propose a hybrid perspective constraint hpc to unify the representation of rigid body and planar motions given a mixture of k hybrid perspective constraints we propose an algebraic process to partition image correspondences to the individual 3 d motions called robust algebraic segmentation ras particularly we prove that the joint distribution of image correspondences is uniquely determined by a set of 2k th degree polynomials a global signature for the union of k motions of possibly mixed type the first and second derivatives of these polynomials provide a means to recover the association of the individual image samples to their respective motions finally using robust statistics we show that the polynomials can be robustly estimated in the presence of moderate image noise and outliers we conduct extensive simulations and real experiments to validate the performance of the new algorithm the results demonstrate that ras achieves notably higher accuracy than most existing robust motion segmentation methods including random sample consensus ransac and its variations the implementation of the algorithm is also two to three times faster than the existing methods the implementation of the algorithm and the benchmark scripts are available at http perception csl illinois edu ras

robust multivariate scattering hurwitz interval polynomials abstract the relationship between multivariate scattering hurwitz polynomials and multivariate complex reactance functions is exploited to prove that a specified set of bivariate interval polynomials is characterizable by the scattering hurwitz property from tests on a finite set of extreme bivariate polynomials specifically it is shown that the cardinality of this finite set when the coefficients are restricted to the field of real numbers is 8 this bivariate result is expected to be generalizable to the n variate case for both the real and the complex coefficient cases if one proceeds with adequate caution

robust finite settling time stabilization of discrete time system with structured uncertainty abstract the robust finite settling time fst stabilization problem is considered for an uncertain discrete time system fst stability is a generalization of the dead beat response 9 which requires that all the external signals as well as internal signals of a feedback system settle to new steady states after a finite time for any step inputs the uncertain discrete time system under consideration is described by a causal real rational function which includes uncertain parameters where the uncertain parameters are restricted to prescribed bounding intervals and enter affine linearly into the coefficients of the transfer functions a necessary and sufficient condition for robust fst stability is presented in terms of a finite of transfer functions the condition leads to a computationally verifiable necessary and sufficient condition for robust fst stabilizability and a systematic procedure for designing a robust fst feedback control system

classification and saliency detection by semi supervised low rank representation in the area of pattern recognition low rank representation lrr is an efficient method in recovering the subspace structure of the dataset however lrr is unsupervised without any label information lrr constructs an informative graph which is then combined with the mature graph based semi supervised learning gssl framework to complete the classification task in this paper we propose a new low rank learning method which constructs the low rank representation matrix utilizing label information to obtain a more informative graph this method integrates the low rank graph construction and the label information propagation processes together thus the optimization of the low rank representation and the soft label prediction function are calculated iteratively at the same time we name this method as semi supervised low rank learning sslrl it enhanced the classification performance of traditional lrr graph based ssl by 5 30 and the running time is reduced from hundreds to less than ten seconds based on this method a new outlier detection strategy is presented this strategy succeeds with an auc of at least 93 even if the detection condition of lrr is not satisfied the effectiveness of sslrl is demonstrated in semi supervised classification outlier detection and salient detection tasks these extensive experimental results highlight the outperforming of our method over state of the art methods highlightsa semi supervised version of low rank representation is presented label information based outlier and saliency detection strategies are presented semi supervised low rank learning is efficient and effective in classification semi supervised low rank learning is reliable in outlier detection

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

on pairwise a s closed spaces abstract in this piece of work the notion of pairwise s closed space is introduced in a sense based on other definitions of pairwise fuzzy semiopenness and pairwise fuzzy regular closedness different from that given by m e abd el monsef and a e ramdan bull fac sci alex 26a 1 1986 18 27 also the image and the inverse image of pairwise s closed spaces under some types of functions are investigated for some special cases a good agreement is achieved between the present investigation and that obtained in 1986 by abd el monsef and ramdan

strong and ultra separation axioms of fuzzy bitopological spaces given a fuzzy bitopological space x 1 2 we introduce a new notion of fuzzy pairwise separation axioms by using the family of its level bitopologies 1 2 0 1 we prove that these concepts are good extension and we compare them with its corresponding fpt kandil and ei shafee 1991 and fpt1 abu safiya et al 1994 i 0 1 2 3 4 respectively we show that these notions are not equivalent and we give a number of examples which illustrate this fact

estimation of subspace arrangements with applications in modeling and segmenting mixed data recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted high dimensional data that have very complicated structures from both geometric and statistical points of view such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model in this paper we propose to use subspace arrangements a union of multiple subspaces for modeling mixed data each subspace in the arrangement is used to model just a homogeneous subset of the data thus multiple subspaces together can capture the heterogeneous structures within the data set in this paper we give a comprehensive introduction to a new approach for the estimation of subspace arrangements this is known as generalized principal component analysis gpca in particular we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust even when the given data are corrupted by noise or contaminated with outliers this new method in many ways improves and generalizes extant methods for modeling or clustering mixed data there have been successful applications of this new method to many real world problems in computer vision image processing and system identification in this paper we will examine several of those representative applications this paper is intended to be expository in nature however in order that this may serve as a more complete reference for both theoreticians and practitioners we take the liberty of filling in several gaps between the theory and the practice in the existing literature

a simplified derivation of the zeheb walach 2 d stability test with applications to time delay systems zeheb and walach gave a stability test for n d systems for 2 d systems a simpler derivation is presented here using the results of decarlo et al it is then shown how the method may also be used to test for stability independent of delay of retarded time delay systems

a geometric analysis of subspace clustering with outliers this paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes as is common in computer vision or unsupervised learning applications we do not know in advance how many subspaces there are nor do we have any information about their dimensions we develop a novel geometric analysis of an algorithm named sparse subspace clustering ssc 11 which signicantly broadens the range of problems where it is provably eective for instance we show that ssc can recover multiple subspaces each of dimension comparable to the ambient dimension we also prove that ssc can correctly cluster data points even when the subspaces of interest intersect further we develop an extension of ssc that succeeds when the data set is corrupted with possibly overwhelmingly many outliers underlying our analysis are clear geometric insights which may bear on other sparse recovery problems a numerical study complements our theoretical analysis and demonstrates the eectiveness of these methods

robust stability of polynomials with multilinear parameter dependence abstract the problem is studied of testing for stability a class of real polynomials in which the coefficients depend on a number of variable parameters in a multilinear way we show that the testing for real unstable roots can be achieved by examining the stability of a finite number of corner polynomials obtained by setting parameters at their extreme values while checking for unstable complex roots normally involves examining the real solutions of up to m 1 simultaneous polynomial equations where m is the number of parameters when m 2 this is an especially simple task

multiframe motion segmentation with missing data using powerfactorization and gpca we consider the problem of segmenting multiple rigid body motions from point correspondences in multiple affine views we cast this problem as a subspace clustering problem in which point trajectories associated with each motion live in a linear subspace of dimension two three or four our algorithm involves projecting all point trajectories onto a 5 dimensional subspace using the svd the powerfactorization method or ransac and fitting multiple linear subspaces representing different rigid body motions to the points in 5 using gpca unlike previous work our approach does not restrict the motion subspaces to be four dimensional and independent instead it deals gracefully with all the spectrum of possible affine motions from two dimensional and partially dependent to four dimensional and fully independent our algorithm can handle the case of missing data meaning that point tracks do not have to be visible in all images by using the powerfactorization method to project the data in addition our method can handle outlying trajectories by using ransac to perform the projection we compare our approach to other methods on a database of 167 motion sequences with full motions independent motions degenerate motions partially dependent motions missing data outliers etc on motion sequences with complete data our method achieves a misclassification error of less that 5 for two motions and 29 for three motions

strictly hurwitz property invariance of quartics under coefficient perturbation in this note it is shown how the maximum interval centered around each of the coefficients of a prescribed fourth degree strictly hurwitz polynomial may be determined so that the strictly hurwitz property remains invariant when each coefficient might be perturbed to any arbitrary value within its permissible interval

robust root clustering for linear uncertain systems using generalized lyapunov theory in this paper the problem of matrix root clustering in sub regions of complex plane for linear state space models with real parameter uncertainty is considered the nominal matrix root clustering theory of gutman and jury 1981 ieee trans aut control ac 26 403 using generalized lyapunov equation is extended to the perturbed matrix case and bounds are derived on the perturbation to maintain root clustering inside a given region the theory allows us to get an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space the current literature available on perturbation bounds for robust stability becomes a special case of this unified theory

a dual result to kharitonov s theorem a dual problem to kharitonov s problem involving a diamond instead of a rectangle is considered the results show that a family of polynomials with coefficients varying in the diamond is strictly hurwitz if and only if eight one dimensional exposed edges of the diamond are strictly hurwitz

enhancing low rank subspace clustering by manifold regularization recently low rank representation lrr method has achieved great success in subspace clustering sc which aims to cluster the data points that lie in a union of low dimensional subspace given a set of data points lrr seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself however lrr only considers the global euclidean structure while the local manifold structure which is often important for many real applications is ignored in this paper to exploit the local manifold structure of the data a manifold regularization characterized by a laplacian graph has been incorporated into lrr leading to our proposed laplacian regularized lrr laplrr an efficient optimization procedure which is based on alternating direction method of multipliers admm is developed for laplrr experimental results on synthetic and real data sets are presented to demonstrate that the performance of lrr has been enhanced by using the manifold regularization

robust schur stability of a polytope of polynomials the main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle the criterion obtained serves as a discrete time counterpart for results in s bialas 1985 and f fu and b r barmish 1987 for the continuous case also the results are reduced to operations on n 1 n 1 matrices it is concluded that by the edge result of a c bartlett et al 1987 it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region d

on robust hurwitz and schur polynomials based on results of a v lipatov and n i sokolov 1979 simple sufficient conditions for the robust stability of both strictly hurwitz and schur interval polynomials are obtained furthermore sufficient conditions are derived for robustness of strictly hurwitz and schur polynomials whose coefficients of linear functions of a single parameter several examples are discussed illustrating the derived results

compactness and weakly induced bifuzzy topological spaces abstract induced and weakly induced fuzzy topological spaces were introduced by martin weakly induced fuzzy topological spaces j math anal appl 78 1980 634 639 compactness in bifuzzy topological spaces were introduced by mashhour et al bifuzzy topological spaces submitted in this paper we introduce other types of compactness induced and weakly induced bifuzzy topological spaces and use an alteration of lowen s good extension criterion to test those definitions

robust recovery of subspace structures by low rank representation in this paper we address the subspace clustering problem given a set of data samples vectors approximately drawn from a union of multiple subspaces our goal is to cluster the samples into their respective subspaces and remove possible outliers as well to this end we propose a novel objective function named low rank representation lrr which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary it is shown that the convex program associated with lrr solves the subspace clustering problem in the following sense when the data is clean we prove that lrr exactly recovers the true subspace structures when the data are contaminated by outliers we prove that under certain conditions lrr can exactly recover the row space of the original data and detect the outlier as well for data corrupted by arbitrary sparse errors lrr can also approximately recover the row space with theoretical guarantees since the subspace membership is provably determined by the row space these further imply that lrr can perform robust subspace clustering and error correction in an efficient and effective way

robust stability of perturbed systems with time delays abstract motivated by dynamical system considerations a number of new results on robust stability of perturbed polynomials have been recently obtained in the literature under consideration the perturbations are known only within given bounds and enter affine linearly into the polynomial coefficients in this paper this formulation is expanded to include time delays under a properness assumption a necessary and sufficient condition for robust stability is developed an example is given to illustrate application of the main result

mixtures of probabilistic principal component analyzers principal component analysis pca is one of the most popular techniques for processing compressing and visualizing data although its effectiveness is limited by its global linearity while nonlinear variants of pca have been proposed an alternative paradigm is to capture data complexity by a combination of local linear pca projections however conventional pca does not correspond to a probability density and so there is no unique way to combine pca models therefore previous attempts to formulate mixture models for pca have been ad hoc to some extent in this article pca is formulated within a maximum likelihood framework based on a specific form of gaussian latent variable model this leads to a well defined mixture model for probabilistic principal component analyzers whose parameters can be determined using an expectationmaximization algorithm we discuss the advantages of this model in the context of clustering density modeling and local dimensionality reduction and we demonstrate its application to image compression and handwritten digit recognition

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

necessary and sufficient conditions for root clustering of a polytope of polynomials in a simply connected domain linear time invariant systems with uncertain parameters are considered a test is given which is both necessary and sufficient for root clustering of a family of polytopic polynomials in a simply connected domain the test does not require checking a continuum of polynomials special cases include stability testing of continuous time systems and of discrete time systems with uncertain parameters as well as relative stability tests of such systems interval polynomials can also be handled as a special case

spectral curvature clustering scc this paper presents novel techniques for improving the performance of a multi way spectral clustering framework govindu in proceedings of the 2005 ieee computer society conference on computer vision and pattern recognition cvpr 05 vol 1 pp 1150 1157 2005 chen and lerman 2007 preprint in the supplementary webpage for segmenting affine subspaces specifically it suggests an iterative sampling procedure to improve the uniform sampling strategy an automatic scheme of inferring the tuning parameter from the data a precise initialization procedure for k means as well as a simple strategy for isolating outliers the resulting algorithm spectral curvature clustering scc requires only linear storage and takes linear running time in the size of the data it is supported by theory which both justifies its successful performance and guides our practical choices we compare it with other existing methods on a few artificial instances of affine subspaces application of the algorithm to several real world problems is also discussed

extreme point robust stability results for discrete time polynomials this paper provides some new extreme point robust stability results for discrete time polynomials with special uncertainties in the coefficient space the proofs obtained using the bilinear transformation are simple and the results specialize to existing robust stability results

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

a note on convex combinations of polynomials we show an equivalence between conditions for linear systems to be stabilizable by stable controllers and conditions for convex combinations of polynomials to be stable

hybrid linear modeling via local best fit flats we present a simple and fast geometric method for modeling data by a union of affine subspaces the method begins by forming a collection of local best fit affine subspaces i e subspaces approximating the data in local neighborhoods the correct sizes of the local neighborhoods are determined automatically by the jones 2 numbers we prove under certain geometric conditions that our method finds the optimal local neighborhoods the collection of subspaces is further processed by a greedy selection procedure or a spectral method to generate the final model we discuss applications to tracking based motion segmentation and clustering of faces under different illuminating conditions we give extensive experimental evidence demonstrating the state of the art accuracy and speed of the suggested algorithms on these problems and also on synthetic hybrid linear data as well as the mnist handwritten digits data and we demonstrate how to use our algorithms for fast determination of the number of affine subspaces

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

robust schur stability of interval polynomials the investigation of schur stability using a kharitonov parameter box is discussed the discrete counterpart of kharitonov s theorem is obtained the solution is based on the use of the hollot bartlett huang theorem and the hollott bartlett theorem this made it possible to test for schur stability only a subset of the edges the schur testing of the required edges of the cube is performed using three different methods namely the critical edge polynomial edge stability as an eigenvalue problem and edge stability using colinearity conditions comparison of these three methods is presented it is believed that with the schur testing of the minimum number of edges and the use of the critical stability constraints minimum computational effort can be achieved

a note on two methods related to stability robustness of polynomials in a sector relative stability two recent results on the stability robustness of uncertain systems polynomials are addressed one gives a vertex test for left sector relative stability where the number of the required vertices is four for a real case and eight for a complex case the other gives an elegant frequency domain graphical hodograph approach for left plane stability where the plotting of only one two for a complex case hodograph plus simple boundary conditions is both necessary and sufficient to obtain the maximum coefficient perturbation bounds it is shown that a similar graphical test exists for the left sector stability case

zero sets of multiparameter functions and stability of multidimensional systems new theorems which can be used to find the zero set of a multiparameter rational function of a complex variable where the distinguished boundary of the parameters closed domain of definition is composed of piecewise smooth jordan arcs or curves are stated and proved the results are used to derive a new simplified procedure for a multi dimensional stability test presented for the continuous analog case as well as for the discrete digital case now proofs to huang s and strintzis theorems on multidimensional stability are also provided as an application of the theorems on zero sets

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

robust stability of control systems with polytopical uncertainty a nyquist approach for technical plants a bounded continuum of parameter values describes admissible process models a robust controller guarantees the observance of minimal requirements for all of the allowed process models in this paper a frequency domain approach is proposed that permits the instability of a family of polynomials to be checked this method can be extended in an easy manner to investigate the instability of a closed loop the plant is thereby described by a family of models with a polytopical region of uncertainty in the parameter space as an important special case of the general d stability the hurwitz stability of the closed loop is investigated and a minimal set of necessary and sufficient conditions for robust hurwitz stability is given a generalization for other stability domains is possible besides an algebraic criterion based on a zero inclusion check for a minimal set of exposed edges of the polytopical region a graphic criterion of nyquist type can also be used

sparse subspace clustering algorithm theory and applications many real world problems deal with collections of high dimensional data such as images videos text and web documents dna microarray data and more often such high dimensional data lie close to low dimensional structures corresponding to several classes or categories to which the data belong in this paper we propose and study an algorithm called sparse subspace clustering to cluster data points that lie in a union of low dimensional subspaces the key idea is that among the infinitely many possible representations of a data point in terms of other points a sparse representation corresponds to selecting a few points from the same subspace this motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces since solving the sparse optimization program is in general np hard we consider a convex relaxation and show that under appropriate conditions on the arrangement of the subspaces and the distribution of the data the proposed minimization program succeeds in recovering the desired sparse representations the proposed algorithm is efficient and can handle data points near the intersections of subspaces another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances such as noise sparse outlying entries and missing entries by incorporating the model of the data into the sparse optimization program we demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real world problems of motion segmentation and face clustering

image representation using laplacian regularized nonnegative tensor factorization tensor provides a better representation for image space by avoiding information loss in vectorization nonnegative tensor factorization ntf whose objective is to express an n way tensor as a sum of k rank 1 tensors under nonnegative constraints has recently attracted a lot of attentions for its efficient and meaningful representation however ntf only sees euclidean structures in data space and is not optimized for image representation as image space is believed to be a sub manifold embedded in high dimensional ambient space to avoid the limitation of ntf we propose a novel laplacian regularized nonnegative tensor factorization lrntf method for image representation and clustering in this paper in lrntf the image space is represented as a 3 way tensor and we explicitly consider the manifold structure of the image space in factorization that is two data points that are close to each other in the intrinsic geometry of image space shall also be close to each other under the factorized basis to evaluate the performance of lrntf in image representation and clustering we compare our algorithm with nmf ntf ncut and gnmf methods on three standard image databases experimental results demonstrate that lrntf achieves better image clustering performance while being more insensitive to noise

on the stability properties of polynomials with perturbed coefficients given a polynomial p c s s n t 1 s n 1 t n 0 which is hurwitz or p d z z n t 1 z n 1 t n 0 which has zeros only within or on the unit circle it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties in this note a method is presented for obtaining the largest hypersphere centered at t t t 1 t n containing only polynomials which are stable

modal control of large flexible space structures using collocated actuators and sensors the authors consider the problem of assigning the eigenvalues associated with critical modes of a large flexible space structure into a specified region in the left half plane via direct velocity feedback control dvfc using collocated actuators and sensors conditions for the existence of a dvfc using collocated actuators and sensors that can achieve the eigenvalue assignment are derived when there exist nonunique feasible dvfcs the one with least frobenius norm feedback gain is determined an experimental four bay truss is used to illustrate the results

a compactness in bifuzzy topological spaces abstract compact fuzzy topological spaces were first introduced by chang 3 compact fuzzy topological spaces were introduced by gantner et al 4 abd el monsef et al 1 introduced the notion of almost compact fuzzy topological spaces mashbour et al 8 introduced the notion of bifuzzy topological spaces and defined the notion of compactness in those spaces in this paper we obtain some new results about compact bifuzzy topological spaces we introduce and study the notion of pairwise almost compact bifuzzy topological spaces