exponential stability and solution bounds for systems with bounded nonlinearities estimation of lyapunov exponents of systems with bounded nonlinearities plays an essential part in their robust control known results in this field are based on the gronwall inequality yielding relatively conservative bounds for lyapunov exponents in this note we obtained more accurate upper bounds for the general lyapunov exponent for systems consisting of a known linear time varying part and an unknown nonlinear component with a bounded lipschitz constant at zero consequently a sufficient condition for exponential stability of this system is formulated the systems are indicated for which the obtained bound is precise i e cannot be improved without additional information on the nonlinear term in the presence of a persisting perturbation an upper bound for the solution norm is derived and expressed in the norm of the solution of the corresponding linear system using the obtained results a condition for exponential stability of a linear time varying control system with a nonlinear feedback is derived numerical results are obtained for a second order time varying system and for the lienard equation in the latter case they are favorably compared with stability conditions previously obtained using the lyapunov function method

automatic face naming by learning discriminative affinity matrices from weakly labeled images given a collection of images where each image contains several faces and is associated with a few names in the corresponding caption the goal of face naming is to infer the correct name for each face in this paper we propose two new methods to effectively solve this problem by learning two discriminative affinity matrices from these weakly labeled images we first propose a new method called regularized low rank representation by effectively utilizing weakly supervised information to learn a low rank reconstruction coefficient matrix while exploring multiple subspace structures of the data specifically by introducing a specially designed regularizer to the low rank representation method we penalize the corresponding reconstruction coefficients related to the situations where a face is reconstructed by using face images from other subjects or by using itself with the inferred reconstruction coefficient matrix a discriminative affinity matrix can be obtained moreover we also develop a new distance metric learning method called ambiguously supervised structural metric learning by using weakly supervised information to seek a discriminative distance metric hence another discriminative affinity matrix can be obtained using the similarity matrix i e the kernel matrix based on the mahalanobis distances of the data observing that these two affinity matrices contain complementary information we further combine them to obtain a fused affinity matrix based on which we develop a new iterative scheme to infer the name of each face comprehensive experiments demonstrate the effectiveness of our approach

a new stability test for nonlinear nonautonomous systems we consider a class of nonlinear nonautonomous systems whose linear parts are slowly varying matrices stability conditions and estimates for the region of attraction of the zero solution are derived these conditions are formulated in terms of the determinants of the variable matrices

brief paper a numerical sufficiency test for the asymptotic stability of linear time varying systems a numerical sufficiency test for the asymptotic stability of linear time varying hurwitz systems is proposed the algorithmic procedure constructs a bounding tube in which the state is guaranteed to stay the continuous time system is evaluated at discrete time instants for which successive quadratic lyapunov functions are generated the tube is constructed based on i a conservative estimate of the state evolution from a discrete time instant to the next obtained from the corresponding lyapunov function and ii re evaluation of the tube diameter at each discrete time instant to account for variations in the plant matrix the numerical test is illustrated in simulation via both a stable and an unstable system

analysis of the fuzzy controllability property and stabilization for a class of t s fuzzy models in this paper the controllability property for a class of takagi sugeno t s fuzzy models is analyzed while a fully nonlinear stabilizer is designed in a practical way it is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach the existence of such controllers depends on the fuzzy controllability conditions which are derived in a straightforward way the main advantage of the proposed approach is that the convergence of the closed loop system can be imposed arbitrarily some examples are given in order to illustrate the validity of the method finally the proposed controller is applied on an underactuated system known as pendubot and the results are compared with an stabilizer designed on the basis of lmis

stability analysis for linear systems with singular second order vector differential equations this technical note is concerned with exponential stability analysis of linear time varying systems represented by the second order vector differential equations with the singular leading coefficient matrix using bounding techniques on the trajectories of the linear time varying systems the stability problem of the time varying systems is transformed to that of the time invariant systems and a new sufficient condition for exponential stability is derived the obtained condition can be applied to the nonsingular case and it is proven that the condition for the nonsingular case is superior to a test presented in the recent literature analogously the proposed method is also extended to the stability analysis for a class of linear time varying systems with delay by illustrative examples better results are obtained by the proposed criteria as compared with some results in the literature

new stability conditions for a class of linear time varying systems this paper considers the problem of asymptotic stability for linear time varying systems of the form x t a t x t some new stability conditions are proposed first two stability conditions for nonlinear time varying systems are given by using non monotonic lyapunov functions then the results obtained are extended to the linear case two stability conditions with infinite integral are derived furthermore by using the top floor function a linear matrix inequalities lmi condition and an eigenvalue criterion for asymptotic stability of systems are presented comparing with the existing results the conditions obtained allow both a t and a t are unbounded at t some numerical examples are provided to show the effectiveness of the theoretical results

gain scheduled and nonlinear systems dynamic analysis by velocity based linearization families a family of velocity based linearizations is proposed for a nonlinear system in contrast to the conventional series expansion linearization a member of the family of velocity based linearizations is valid in the vicinity of any operating point not just an equilibrium operating point the velocity based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated using velocity based linearizations stability conditions are derived for both smooth and non smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily perhaps excessively small neighbourhood about the equilibrium operating points inherent in existing frozen input theory for systems where there is no restriction on the rate of variation the velocity based linearization analysis is global in nature the analysis techniques developed although quite general are motivated by the gain scheduling design

new sufficient conditions for the stability of slowly varying linear systems the frozen time approach is used to state some new sufficient conditions for the stability of linear time varying systems an upper bound on the norm of the time derivative of system matrix which under different assumptions on frozen time system eigenvalues guarantees asymptotic stability or exponential stability of the system is established

some characterizations of symmetric inverse m matrices abstract we apply the previously proved equivalence of four models to present new characterizations of matrices whose inverse is a weakly diagonally dominant symmetric m matrix it is shown that the case of strictly ultrametric matrices of martinez michon and san martin is included as a corollary

an approximate solution for linear boundary value problems with slowly varying coefficients in this paper an approximate closed form solution for linear boundary value problems with slowly varying coefficient matrices is obtained the derivation of the approximate solution is based on the freezing technique which is commonly used in analyzing the stability of slowly varying initial value problems as well as solving them the error between the approximate and the exact solutions is given and an upper bound on the norm of the error is obtained this upper bound is proportional to the rate of change of the coefficient matrix of the boundary value problem the proposed approximate solution is obtained for a two point boundary value problem and is compared to its solution obtained numerically good agreement is observed between the approximate and the numerical solutions when the rate of change of the coefficient matrix is small

a less conservative stability test for second order linear time varying vector differential equations system stability and stability bounds play an essential role in control theory this note is concerned with the exponential stability of a class of second order linear time varying vector differential equations with real piecewise continuous coefficient matrices a less conservative explicit condition for stability of such a system is derived using the matrix measure theory and a more accurate upper bound for the decay exponent of its stable solution is established examples are included for illustration

nonnegative blind source separation by sparse component analysis based on determinant measure the problem of nonnegative blind source separation nbss is addressed in this paper where both the sources and the mixing matrix are nonnegative because many real world signals are sparse we deal with nbss by sparse component analysis first a determinant based sparseness measure named d measure is introduced to gauge the temporal and spatial sparseness of signals based on this measure a new nbss model is derived and an iterative sparseness maximization ism approach is proposed to solve this model in the ism approach the nbss problem can be cast into row to row optimizations with respect to the unmixing matrix and then the quadratic programming qp technique is used to optimize each row furthermore we analyze the source identifiability and the computational complexity of the proposed ism qp method the new method requires relatively weak conditions on the sources and the mixing matrix has high computational efficiency and is easy to implement simulation results demonstrate the effectiveness of our method

an alternate stability analysis framework for adaptive control n abstract a proof is given for the uniform asymptotic stability of a class of pointwise in time stable systems of time varying ordinary differential equations the sufficient conditions for stability are shown to be naturally testable in a general adaptive control context a weak form of robust identification is found to imply robust stability of the overall closed loop adaptive control system

improved error bounds for freezing solutions of linear boundary value problems for the error in the freezing solutions of linear boundary value problems we obtain a bound which is sharper than that obtained recently by shahruz and schwartz appl math comput 60 1994 285 comput math appl 28 1994 75 a different freezing technique global freezing is also proposed it is shown that this new technique is easy to implement for numerical computation of the solutions moreover the corresponding solution has an error bound similar to that of the freezing method

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

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

assessing asymptotic stability of linear continuous time varying systems by computing the envelope of all trajectories in this note necessary and sufficient numerical conditions for asymptotic stability and for uniform asymptotic stability of linear continuous time varying systems are derived for a given set of initial conditions a tube containing all the trajectories of the system is constructed in the state space at each instant of time there exists an initial condition inside the set such that the resulting trajectory attains the border of the tube based on the above formulation necessary and sufficient conditions for asymptotic stability and for uniform asymptotic stability are expressed through the solution of a linear differential lyapunov equation the conditions can deal with the stability of periodic systems as well one of the main characteristics of the proposed necessary and sufficient conditions is that the only assumption on the dynamical matrix of the time varying system is continuity examples from the literature illustrate the superiority of the proposed conditions when compared to other methods

resistance distances in extended or contracted networks abstract in this paper we introduce new effective resistances on a given network associated with a positive value and two weights on the vertex set and investigate under which conditions they determine a distance we prove that this property is closely related with superharmonicity moreover we analyze the behavior of these distances under the usual network transformations specially the so called star mesh transformation we also compute the effective resistance for an extended network that is the network obtained from the former one by joining a new vertex and then study the effect of the contraction of this new network that is we apply a star mesh transformation with center in the joined vertex

stability and instability matrices for linear evolution variational inequalities this paper deals with the characterization of the stability and instability matrices for a class of unilaterally constrained dynamical systems represented as linear evolution variational inequalities levi such systems can also be seen as a sort of differential inclusion or in special cases as linear complementarity systems which in turn are a class of hybrid dynamical systems examples show that the stability of the unconstrained system and that of the constrained system may drastically differ various criteria are proposed to characterize the stability or the instability of levi

kirchhoff indexes of a network in this work we define the effective resistance between any pair of vertices with respect to a value 0 and a weight on the vertex set this allows us to consider a generalization of the kirchhoff index of a finite network it turns out that is the lowest eigenvalue of a suitable semi definite positive schrodinger operator and is the associated eigenfunction we obtain the relation between the effective resistance and hence between the kirchhoff index with respect to and and the eigenvalues of the associated schrodinger operator however our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures of the network from these expressions we derive a full generalization of foster s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk finally we compute the effective resistances and the generalized kirchhoff index with respect to a and for some families of networks with symmetries specifically for weighted wagon wheels and circular ladders

relaxed conditions for the exponential stability of a class of linear time varying systems this technical note states new sufficient conditions for the exponential stability of linear time varying ltv systems of the form aeligmacr ldr a t aelig t the approach proposed derives and uses the notion of perturbed frozen time pft form that can be associated to any ltv system exploiting the bellman gronwall lemma relaxed stability conditions are then stated in terms of ldquoaveragerdquo parameter variations salient features of the approach are pointwise stability of a ldr is not required amacr ldr may not be bounded the stability conditions also apply to uncertain systems the approach is illustrated by numerical examples

stability analysis of dynamical neural networks in this paper we use the matrix measure technique to study the stability of dynamical neural networks testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given it shows how a few well known results can be unified and generalized in a straightforward way local exponential stability of a class of dynamical neural networks is also studied we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point from this some well known and new sufficient conditions for local exponential stability of neural networks are obtained

unified stability criteria for slowly time varying and switched linear systems this paper presents a unified approach to formulating stability conditions for slowly time varying linear systems and switched linear systems the concept of total variation is generalized to the case of matrix valued functions using this generalized concept a result extending existing stability conditions for slowly time varying linear systems is derived as special cases of this result two sets of stability conditions are derived for switched linear systems which match known results in the literature a numerical example is included to further illustrate the application of the main result

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

l and l 2 semi global stabilisation of continuous time periodic linear systems with bounded controls this article is concerned with l and l 2 semi global stabilisation of continuous time periodic linear systems with bounded controls two problems namely l semi global stabilisation with controls having bounded magnitude and l 2 semi global stabilisation with controls having bounded energy are solved based on solutions to a class of periodic lyapunov differential equations pldes resulting from the problem of minimal energy control with guaranteed convergence rate under the assumption that the open loop system is asymptotically null controllable with constrained controls periodic feedback are established to solve the concerned problems the proposed plde based approaches possess the advantage that the resulting controllers are easy to implement since the designers need only to solve a linear differential equation a numerical example is worked out to illustrate the effectiveness of the proposed approach

a note on uniform exponential stability of linear periodic time varying systems in this paper we derive a new criterion for uniform stability assessment of the linear periodic time varying systems dot x a t x and a t t a t as a corollary the lower and upper bounds for the floquet characteristic exponents are established the approach is based on the use of logarithmic norm of the system matrix a t finally we analyze the robustness of the stability property under external disturbance

minimizing effective resistance of a graph the effective resistance between two nodes of a weighted graph is the electrical resistance seen between the nodes of a resistor network with branch conductances given by the edge weights the effective resistance comes up in many applications and fields in addition to electrical network analysis including for example markov chains and continuous time averaging networks in this paper we study the problem of allocating edge weights on a given graph in order to minimize the total effective resistance i e the sum of the resistances between all pairs of nodes we show that this is a convex optimization problem and can be solved efficiently either numerically or in some cases analytically we show that optimal allocation of the edge weights can reduce the total effective resistance of the graph compared to uniform weights by a factor that grows unboundedly with the size of the graph we show that among all graphs with n nodes the path has the largest value of optimal total effective resistance and the complete graph has the least

low rank structure learning via nonconvex heuristic recovery in this paper we propose a nonconvex framework to learn the essential low rank structure from corrupted data different from traditional approaches which directly utilizes convex norms to measure the sparseness our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low rank structure and the sparse corruptions we will respectively introduce how to combine the widely used lp norm 0 p 1 and log sum term into the framework of low rank structure learning although the proposed optimization is no longer convex it still can be effectively solved by a majorization minimization mm type algorithm with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches we prove that the mm type algorithm can converge to a stationary point after successive iterations the proposed model is applied to solve two typical problems robust principal component analysis and low rank representation experimental results on low rank structure learning demonstrate that our nonconvex heuristic methods especially the log sum heuristic recovery algorithm generally perform much better than the convex norm based method 0 p 1 for both data with higher rank and with denser corruptions

design of controllers for linear parameter varying systems by the gain scheduling technique abstract design of controllers for linear multi input multi output systems whose dynamics depend on a time varying parameter is studied design algorithms for the state feedback control law based on the gain scheduling technique are proposed state feedback control laws are designed so that one of the following goals is achieved i the poles of the closed loop system for all fixed parameter values are placed in a small neighborhood of a set of desired closed loop poles ii the stability of the closed loop system for all fixed parameter values guarantees that the of the system with the time varying parameter independent of the rate of change of the parameter rigorously justified and computationally appealing design algorithms are developed

stabilisation of time varying linear systems via lyapunov differential equations this article studies stabilisation problem for time varying linear systems via state feedback two types of controllers are designed by utilising solutions to lyapunov differential equations the first type of feedback controllers involves the unique positive definite solution to a parametric lyapunov differential equation which can be solved when either the state transition matrix of the open loop system is exactly known or the future information of the system matrices are accessible in advance different from the first class of controllers which may be difficult to implement in practice the second type of controllers can be easily implemented by solving a state dependent lyapunov differential equation with a given positive definite initial condition in both cases explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed loop systems numerical examples show the effectiveness of the proposed approaches

integrated low rank based discriminative feature learning for recognition feature learning plays a central role in pattern recognition in recent years many representation based feature learning methods have been proposed and have achieved great success in many applications however these methods perform feature learning and subsequent classification in two separate steps which may not be optimal for recognition tasks in this paper we present a supervised low rank based approach for learning discriminative features by integrating latent low rank representation latlrr with a ridge regression based classifier our approach combines feature learning with classification so that the regulated classification error is minimized in this way the extracted features are more discriminative for the recognition tasks our approach benefits from a recent discovery on the closed form solutions to noiseless latlrr when there is noise a robust principal component analysis pca based denoising step can be added as preprocessing when the scale of a problem is large we utilize a fast randomized algorithm to speed up the computation of robust pca extensive experimental results demonstrate the effectiveness and robustness of our method

quadratic stabilizability of a new class of linear systems with structural independent time varying uncertainty this paper investigates the problem of designing a linear state feedback control to stabilize a new class of single input uncertain linear dynamical systems uncertain parameters in the system matrices are time varying and bounded in given compact sets we first provide a concept called new standard system where some of the entries are required to be negative sign invariant and sign invariant and each entry varies independently in an arbitrarily large range then for a class of new standard systems we derive a necessary and sufficient condition under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the result extends the main result in wei 1990 ieee transactions on automatic control 35 3 268 277

on asymptotic stability of linear time varying systems this paper is concerned with asymptotic stability analysis of linear time varying ltv systems with the help of the notion of stable functions some differential lyapunov inequalities dlis based necessary and sufficient conditions are derived for testing asymptotic stability exponential stability and uniformly exponential stability of general ltv systems with the help of the concept of non uniformly exponential stability a class of upper triangular ltv systems is carefully investigated based on the developed stability analysis approaches a couple of numerical examples with some of them borrowed from the literature is provided to illustrate the effectiveness of the proposed theoretical results

mrm lasso a sparse multiview feature selection method via low rank analysis learning about multiview data involves many applications such as video understanding image classification and social media however when the data dimension increases dramatically it is important but very challenging to remove redundant features in multiview feature selection in this paper we propose a novel feature selection algorithm multiview rank minimization based lasso mrm lasso which jointly utilizes lasso for sparse feature selection and rank minimization for learning relevant patterns across views instead of simply integrating multiple lasso from view level we focus on the performance of sample level sample significance and introduce pattern specific weights into mrm lasso the weights are utilized to measure the contribution of each sample to the labels in the current view in addition the latent correlation across different views is successfully captured by learning a low rank matrix consisting of pattern specific weights the alternating direction method of multipliers is applied to optimize the proposed mrm lasso experiments on four real life data sets show that features selected by mrm lasso have better multiview classification performance than the baselines moreover pattern specific weights are demonstrated to be significant for learning about multiview data compared with view specific weights

absolute exponential stability of a class of continuous time recurrent neural networks this paper presents a new result on absolute exponential stability aest of a class of continuous time recurrent neural networks with locally lipschitz continuous and monotone nondecreasing activation functions the additively diagonally stable connection weight matrices are proven to be able to guarantee aest of the neural networks the aest result extends and improves the existing absolute stability and aest ones in the literature

descriptor learning via supervised manifold regularization for multioutput regression multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis however due to the huge image variability and ambiguity it is fundamentally challenging to handle the highly complex input target relationship of multioutput regression especially with indiscriminate high dimensional representations in this paper we propose a novel supervised descriptor learning sdl algorithm for multioutput regression which can establish discriminative and compact feature representations to improve the multivariate estimation performance the sdl is formulated as generalized low rank approximations of matrices with a supervised manifold regularization the sdl is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low dimensional space aligned to targets the achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression which enables more accurate and efficient multivariate estimation we conduct extensive evaluation of the proposed sdl on both synthetic data and real world multioutput regression tasks for both computer vision and medical image analysis experimental results have shown that the proposed sdl can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts our method establishes a novel sdl framework for multioutput regression which can be widely used to boost the performance in different applications

an approximate solution for homogeneous boundary value problems with slowly varying coefficient matrices abstract in this paper an approximate closed form solution for homogeneous boundary value problems with slowly varying coefficient matrices is obtained the derivation of the approximate solution is based on the freezing technique which is commonly used in analyzing the stability of slowly varying initial value problems as well as solving them the error between the approximate and the exact solutions is given and an upper bound on the norm of the error is obtained this upper bound is proportional to the rate of change of the coefficient matrix of the boundary value problem the proposed approximate solution is obtained for a two point boundary value problem and is compared to its solution obtained numerically good agreement is observed between the approximate and the numerical solutions when the rate of change of the coefficient matrix is small

sufficient conditions for stability of linear time varying systems abstract in this paper we consider sufficient conditions for the exponential stability of linear time varying systems of the form dot x t a t x t t 0 stability guaranteeing upper bounds for different measures of parameter variations are derived

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

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

robust face recognition based on dynamic rank representation abstract robust face recognition is an active topic in computer vision while face occlusion is one of the most challenging problems for robust face recognition algorithm the latest research on low rank representation demonstrated its high efficiency to subspace segmentation and feature extraction motivated by previous work in this paper we consider the problem of human face recognition from frontal views with varying illumination as well as occlusion and disguise we present a novel approach for face recognition by extracting dynamic subspace of images and obtaining the discriminative parts in each individual we use these parts to represent the characteristic of discriminative components give a recognition protocol to classify face images the experiments carried on publicly available databases i e ar extended yale b and orl vilidate its accuray robustness and speed the proposed method needs lower dimensions training samples but gains a higher recognition rate than other popular approaches

robust pca via ell _ 0 ell _ 1 regularization we study the problem of low rank and sparse decomposition from possibly noisy observations known as robust pca where the sparse component can be seen as outliers we first propose a modified objective function where the nuclear norm captures the low rank term ell 0 norm addresses the sparse outlier term and an ell 1 norm to deal with the additive noise term the associated algorithm termed sparsity regularized principal component pursuit srpcp is shown to converge under certain model and algorithm parameter settings it is shown that srpcp can recover the low rank component and sparse component exactly in the noiseless case in the noisy case we first prove that the widely used principal component pursuit pcp method which was designed for the noiseless case is actually stable to dense noise then we show that srpcp has smaller estimation error bound and can identify outlier entries without any false alarm another important byproduct of our analysis is the result that pcp with missing entries is also stable to dense noise we further propose another objective function which replaces the above nuclear norm by the log determinant the proposed algorithm termed iterative reweighted sparsity regularized principal component pursuit is also shown to converge in each iteration it solves a weighted nuclear norm regularized robust matrix completion problem we propose an alternating direction method of multipliers algorithm to solve this nonconvex subproblem which also converges empirical studies demonstrate the efficacy of the proposed ell 0 ell 1 regularization framework to deal with the outliers as well as its advantage over the existing state of the art methods

control of slowly varying linear systems state feedback control of slowly varying linear continuous time and discrete time systems with bounded coefficient matrices is studied in terms of the frozen time approach this study centers on pointwise stabilizable systems these are systems for which there exists a state feedback gain matrix placing the frozen time closed loop eigenvalues to the left of a line re s gamma

variable selection using mm algorithms variable selection is fundamental to high dimensional statistical modeling many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and or nonconcave this article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions these algorithms operate by perturbing the penalty function slightly to render it differentiable then optimizing this differentiable function using a minorize maximize mm algorithm mm algorithms are useful extensions of the well known class of em algorithms a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for em algorithms in particular we prove that when our mm algorithms converge they must converge to a desirable point we also discuss conditions under which this convergence may be guaranteed we exploit the newton raphson like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators our method performs well in numerical tests

on the stability and control of nonlinear dynamical systems via vector lyapunov functions vector lyapunov theory has been developed to weaken the hypothesis of standard lyapunov theory in order to enlarge the class of lyapunov functions that can be used for analyzing system stability in this paper we extend the theory of vector lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states furthermore we present a generalized convergence result which in the case of a scalar comparison system specializes to the classical krasovskii lasalle invariant set theorem in addition we introduce the notion of a control vector lyapunov function as a generalization of control lyapunov functions and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector lyapunov function moreover using control vector lyapunov functions we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel furthermore we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law finally the proposed control framework is used to construct decentralized controllers for large scale nonlinear systems with robustness guarantees against full modeling uncertainty

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

brief on exponential stability of nonlinear time varying differential equations within the liapunov framework a sufficient condition for exponential stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the liapunov function taken along solutions of the system may have positive and negative values verification of the conditions of the main theorem may be harder than in the classical case it is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time varying systems this sets the stability study by means of averaging in a liapunov context in particular it is established that exponential stability of the averaged system implies exponential stability of the original fast time varying system a comparison of our work with results taken from the literature is included

robust subspace segmentation via nonconvex low rank representation a nonconvex formulation to determine the low rank representation from contaminated data is proposed we provide a proximal iteratively reweighed algorithm for solving the nonconvex model the proposed nonconvex model can recover the underlying low rank structure of subspaces in spite of noisy corruptions recently low rank representation lrr has been successfully applied to explore subspace segmentation of data in this paper we propose a nonconvex formulation to determine the lrr from contaminated data unlike in traditional methods which directly utilize the nuclear norm to approximate the rank function and penalize noise using the 2 1 norm our method introduces the ky fan p k norm and the 2 q norm to better approximate the rank minimization problem and enhance the robustness against noise an efficient algorithm is derived for solving the novel objective function and this is followed by a rigorous theoretical proof of the convergence extensive experiments on face datasets clearly demonstrate that the proposed methods are more robust to illumination variations corruptions and occlusions

discrete elliptic operators and their green operators abstract semi definite positive schrodinger operators on finite connected networks are particular examples of a general class of self adjoint operators called elliptic operators any elliptic operator defines an automorphism on the subspace orthogonal to the eigenfunctions associated with the lowest eigenvalue whose inverse is called orthogonal green operator our aim is to study the effect of a perturbation of an elliptic operator on its orthogonal green operator the perturbation here considered is performed by adding a self adjoint and positive semi definite operator we show that schrodinger operators on networks that are obtained by adding weighted edges to a given network can be seen as perturbations of the schrodinger operators on the original network therefore we can compute the green function the effective resistances and the kirchhoff index of a perturbed network in terms of the corresponding ones on the original network we apply the obtained results to the study of perturbations of a weighted star which includes as particular cases the wheel and fan networks

characterization of symmetric m matrices as resistive inverses abstract we aim here at characterizing those nonnegative matrices whose inverse is an irreducible stieltjes matrix specifically we prove that any irreducible stieltjes matrix is a resistive inverse to do this we consider the network defined by the off diagonal entries of the matrix and we identify the matrix with a positive definite schrodinger operator whose ground state is determined by the lowest eigenvalue of the matrix and the corresponding positive eigenvector we also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric m matrices

robust tracking of linear mimo time varying systems abstract the asymptotic properties of the linear multivariable time varying tracking systems constructed from the fixed degree matrix polynomials under the unmodeled dynamics and external disturbances are investigated in this paper the robust controllers are designed based on the frozen time approach first the robust stabilization is assured the asymptotic robust stability conditions on both the mismodeling errors which only depend on the frozen time computations and the variation rates of the perturbed plants are found and quantitatively characterized and more essentially the robust tracking performance is achieved it is shown that if the time varying plants and the time varying nominal models are asymptotically slowly varying then the exact tracking requirement which has zero steady reference command signals tracking errors is achieved in the time varying feedback systems under the situations of the unmodeled dynamics external disturbances and time varying effects of the systems the corresponding permissible ranges of mismodeling errors and the robustness enhancement are provided and discussed

majorization minimization algorithms for wavelet based image restoration standard formulations of image signal deconvolution under wavelet based priors regularizers lead to very high dimensional optimization problems involving the following difficulties the non gaussian heavy tailed wavelet priors lead to objective functions which are nonquadratic usually nondifferentiable and sometimes even nonconvex the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet based denoising this paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems placing them in a common majorization minimization mm framework one of the classes of algorithms considered when using quadratic bounds on nondifferentiable log priors shares the infamous singularity issue si of iteratively re weighted least squares irls algorithms the possibility of having to handle infinite weights which may cause both numerical and convergence issues in this paper we prove several new results which strongly support the claim that the si does not compromise the usefulness of this class of algorithms exploiting the unified mm perspective we introduce a new algorithm resulting from using bounds for nonconvex regularizers the experiments confirm the superior performance of this method when compared to the one based on quadratic majorization finally an experimental comparison of the several algorithms reveals their relative merits for different standard types of scenarios

feature extraction by learning lorentzian metric tensor and its extensions we develop a supervised dimensionality reduction method called lorentzian discriminant projection ldp for feature extraction and classification our method represents the structures of sample data by a manifold which is furnished with a lorentzian metric tensor different from classic discriminant analysis techniques ldp uses distances from points to their within class neighbors and global geometric centroid to model a new manifold to detect the intrinsic local and global geometric structures of data set in this way both the geometry of a group of classes and global data structures can be learnt from the lorentzian metric tensor thus discriminant analysis in the original sample space reduces to metric learning on a lorentzian manifold we also establish the kernel tensor and regularization extensions of ldp in this paper the experimental results on benchmark databases demonstrate the effectiveness of our proposed method and the corresponding extensions

frequency domain criteria of robust stability for slowly time varying systems the problem of stability of feedback systems with structured slowly time varying uncertain gains is considered for the case when the pair uncertain gain derivative belongs to a given convex set a sufficient frequency domain condition of stability is obtained this condition is an mimo generalization of the siso results derived in the 60s in the context of the positivity theory

response of linear slowly varying systems under external excitations abstract an approximate closed form solution for a linear slowly varying system under external excitation is derived the derivation of the solution is based on the technique of freezing slowly varying parameters a technique used in establishing the stability of slowly varying homogeneous systems the error between the approximate and exact solutions is given and an upper bound on the norm of the error in terms of a measure of the rate of change of the system matrix and the norm of the exact solution of the system is derived approximate responses of two particular linear slowly varying systems under external excitation are obtained by the proposed technique good agreement between the approximate and numerically obtained solutions is observed

a gradient algorithm locally equivalent to the em algorithm in many problems of maximum likelihood estimation it is impossible to carry out either the e step or the m step of the em algorithm the present paper introduces a gradient algorithm that is closely related to the em algorithm this em gradient algorithm approximately solves the m step of the em algorithm by one iteration of newton s method since newton s method converges quickly the local properties of the em gradient algorithm are almost identical with those of the em algorithm any strict local maximum point of the observed likelihood locally attracts the em and em gradient algorithm at the same rate of convergence and near the maximum point the em gradient algorithm always produces an increase in the likelihood with proper modification the em gradient algorithm also exhibits global convergence properties that are similar to those of the em algorithm our proof of global convergence applies and improves existing theory for the em algorithm these theoretical points are reinforced by a discussion of three realistic examples illustrating how the em gradient algorithm can succeed where the em algorithm is intractable

some more interplay of the three kirchhoffian indices for any simple connected undirected graph and the random walk on it we obtain a formula for the sum of all expected hitting times normalized by the stationary distribution expressed in terms of the eigenvalues of a certain modified laplacian matrix this allows us to find lower bounds for these sums of hitting times as well as new lower bounds for the additive degree kirchhoff index in terms of the multiplicative degree kirchhoff index and the kirchhoff index that improve other bounds found in the literature

unified low rank matrix estimate via penalized matrix least squares approximation low rank matrix estimation arises in a number of statistical and machine learning tasks in particular the coefficient matrix is considered to have a low rank structure in multivariate linear regression and multivariate quantile regression in this paper we propose a method called penalized matrix least squares approximation pmlsa toward a unified yet simple low rank matrix estimate specifically pmlsa can transform many different types of low rank matrix estimation problems into their asymptotically equivalent least squares forms which can be efficiently solved by a popular matrix fast iterative shrinkage thresholding algorithm furthermore we derive analytic degrees of freedom for pmlsa with which a bayesian information criterion bic type criterion is developed to select the tuning parameters the estimated rank based on the bic type criterion is verified to be asymptotically consistent with the true rank under mild conditions extensive experimental studies are performed to confirm our assertion

structure constrained low rank representation benefiting from its effectiveness in subspace segmentation low rank representation lrr and its variations have many applications in computer vision and pattern recognition such as motion segmentation image segmentation saliency detection and semisupervised learning it is known that the standard lrr can only work well under the assumption that all the subspaces are independent however this assumption cannot be guaranteed in real world problems this paper addresses this problem and provides an extension of lrr named structure constrained lrr sc lrr to analyze the structure of multiple disjoint subspaces which is more general for real vision data we prove that the relationship of multiple linear disjoint subspaces can be exactly revealed by sc lrr with a predefined weight matrix as a nontrivial byproduct we also illustrate that sc lrr can be applied for semisupervised learning the experimental results on different types of vision problems demonstrate the effectiveness of our proposed method

stability of linear nonautonomous multivariable systems with differentiable matrices abstract we consider linear nonautonomous multivariable systems with differentiable matrices explicit stability conditions are derived in the appropriate situations our results improve the traditional freezing method

graph laplace for occluded face completion and recognition this paper proposes a spectral graph based algorithm for face image repairing which can improve the recognition performance on occluded faces the face completion algorithm proposed in this paper includes three main procedures 1 sparse representation for partially occluded face classification 2 image based data mining and 3 graph laplace gl for face image completion the novel part of the proposed framework is gl as named from graphical models and the laplace equation and can achieve a high quality repairing of damaged or occluded faces the relationship between the gl and the traditional poisson equation is proven we apply our face repairing algorithm to produce completed faces and use face recognition to evaluate the performance of the algorithm experimental results verify the effectiveness of the gl method for occluded face completion

a necessary condition for quantitative exponential stability of linear state space systems for an arbitrary n nconstant matrix a the two following facts are well known 1 n re tracea maxj 1 nre j a 0 if u is a unitary matrix one can always find a skew hermitian matrix a so that u ea in this note we present the extension of these two facts to the context of linear time varying dynamical systems x a t x t 0 as a by product this result suggests that the notion of slowly varying state space systems commonly used in literature is mathematically not natural to the problem of exponential stability

stability of linear systems governed by second order vector differential equations we consider linear non autonomous systems governed by second order vector ordinary differential equations explicit stability conditions are derived

sparse approximation to the eigensubspace for discrimination two dimensional 2 d image matrix based projection methods for feature extraction are widely used in many fields of computer vision and pattern recognition in this paper we propose a novel framework called sparse 2 d projections s2dp for image feature extraction different from the existing 2 d feature extraction methods s2dp iteratively learns the sparse projection matrix by using elastic net regression and singular value decomposition theoretical analysis shows that the optimal sparse subspace approximates the eigensubspace obtained by solving the corresponding generalized eigenequation with the s2dp framework many 2 d projection methods can be easily extended to sparse cases moreover when each row column of the image matrix is regarded as an independent high dimensional vector 1 d vector it is proven that the vector based eigensubspace is also approximated by the sparse subspace obtained by the same method used in this paper theoretical analysis shows that when compared with the vector based sparse projection learning methods s2dp greatly saves both computation and memory costs this property makes s2dp more tractable for real world applications experiments on well known face databases indicate the competitive performance of the proposed s2dp over some 2 d projection methods when facial expressions lighting conditions and time vary