comparison of fuzzy numbers based on the probability measure of fuzzy events abstract most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only and suffer from lack of discrimination and occasionally conflict with intuition it is true that fuzzy numbers are frequently partial order and cannot be compared however this does not alleviate the need for comparison in practical applications in this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to zadeh it considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions the approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number it is shown that several comparison indices in the literature can be obtained based on the probability present measure approach finally some typical examples are used to compare the various different approaches the different interpretations of the dispersion index under different physical situations are emphasized

analysis and design of impulsive control systems some sufficient conditions for asymptotic stability of impulsive control systems with impulses at fixed times have recently been presented in this paper we derive some less conservative conditions for asymptotic stability of such impulsive control systems and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also extended

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

analyzing the robustness of impulsive synchronization coupled by linear delayed impulses in this technical note a class of autonomous impulsive differential systems with linear delayed impulses is considered sufficient conditions required for this particular class of systems with varying and constant impulse durations to be equi attractive in the large are obtained these conditions are then applied to impulsively synchronize two coupled chaotic systems by using delayed impulses and a robustness analysis of the model is also provided simulation results are given to demonstrate the analytical results

fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost in this paper a guaranteed cost fuzzy impulsive control gcfic problem is addressed for uncertain continuous time nonlinear systems which can be represented by the takagi sugeno t s fuzzy model with parametric uncertainties based on the t s fuzzy model a novel time varying lyapunov function is initially constructed to derive the existence condition of guaranteed cost fuzzy impulsive controllers which cannot only exponentially stabilize the uncertain fuzzy system but also provide an upper bound on the quadratic cost function then two procedures for designing suboptimal guaranteed cost fuzzy impulsive controllers are given in the sense of minimizing an upper bound of the cost function one casts the controller design into a parameter dependent linear matrix inequality lmi optimization problem and the other casts the controller design into a sequential minimization problem subject to lmi constraints by using the cone complementary linearization ccl algorithm finally an example is presented to illustrate the effectiveness of the proposed method

construction of lyapunov krasovskii functionals for switched nonlinear systems with input delay abstract this paper studies the stability issue for switched nonlinear systems with input delay and disturbance it is assumed that for the nominal system an exponential stabilizing controller is predesigned such that the switched system is stable under a certain switching signal and a piecewise lyapunov function for the corresponding closed loop system is known however in the presence of input delay and disturbance the system may be unstable under the same switching signal for this case a new lyapunov krasovskii functional is firstly constructed based on the known lyapunov function then by employing this new functional a new switching signal satisfying the new average dwell time conditions is constructed to guarantee the input to state stability of the system under a certain delay bound the bound on the average dwell time is closely related to the bound on the input delay finally numerical examples are given to illustrate the effectiveness of the proposed theory

stability of discrete time delayed impulsive linear systems with application to multi tracking this paper studies the stability issue for discrete time delayed impulsive systems ddis the ddis model is formulated from a discrete time delayed system with impulses by using the matrix spectrum theory the estimates of solution with growth exponent are derived for delayed difference inequalities based on these results two types of criteria on exponential stability with an estimated convergence rate have been established for ddis the first type investigates the effect of destabilising impulses while the second is for the case in which the impulses stabilise the unstable discrete time delayed systems as the application the stability results are used to solve the multi tracking issue for discrete time dynamical networks by mixed impulsive networked control minc in which the impulsive control signals are transmitted via a communication network the effect of data dropout of impulsive control signals is also investigated and the maximal allowable dropout rate is estimated for the designed minc

decision risk analysis for an interval topsis method abstract topsis is a multi attribute decision making madm technique for ranking and selection of a number of externally determined alternatives through distance measures when the collected data for each criterion is interval and the risk attitude for a decision maker is unknown we present a new topsis method for normalizing the collected data and ranking the alternatives the results show that the decision maker with different risk attitude ranks the different alternatives

stability of solutions for stochastic impulsive systems via comparison approach this note studies stability problem of solutions for stochastic impulsive systems by employing lyapunov like function method and it s formula comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established based on these comparison principles the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system as the application the stability results are used to design impulsive control for the stabilization of unstable stochastic systems finally one example is given to illustrate the obtained results

sampling from large matrices an approach through geometric functional analysis we study random submatrices of a large matrix a we show how to approximately compute a from its random submatrix of the smallest possible size o rlog r with a small error in the spectral norm where r e vav2f vav22 is the numerical rank of a the numerical rank is always bounded by and is a stable relaxation of the rank of a this yields an asymptotically optimal guarantee in an algorithm for computing low rank approximations of a we also prove asymptotically optimal estimates on the spectral norm and the cut norm of random submatrices of a the result for the cut norm yields a slight improvement on the best known sample complexity for an approximation algorithm for max 2csp problems we use methods of probability in banach spaces in particular the law of large numbers for operator valued random variables

global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency abstract this paper investigates the global exponential stability of impulsive systems with infinite distributed delay by introducing two auxiliary functions and two essential lemmas some sufficient conditions of stability are presented based on flexible impulse frequency where impulses are considered as perturbations when the interval between two consecutive impulse times is very small in some time domains our result just asks that it meets our proposed conditions which is different from some exist results the effectiveness of our result is demonstrated through two simulation examples

synchronization of linear dynamical networks on time scales this paper studies the synchronization problem of complex dynamical networks cdns on time scales a pinning impulsive control scheme that takes into account of time delay effects is designed to achieve synchronization of cdns on time scales with the state of an isolated node based on the theory of time scales and the direct lyapunov method a synchronization criterion is established for linear cdns on general time scales our result shows that by impulsive control a small portion of nodes the consensus of cdns on time scales can be achieved according to our pinning impulsive control scheme different numbers of nodes will be selected at each impulsive instant and time delay is considered in the pinning impulses the modeling framework developed in this paper is a unification and generalization of many existing continuous time and discrete time cdn models while the pinning impulsive control scheme is an extension of the existing control scheme for synchronization of continuous time cdns moreover the idea of studying dynamical systems on time scales provide a unified approach to investigate continuous time system and its discrete time counterpart simultaneously numerical simulations are given to illustrate the effectiveness of the theoretical analysis

spectral regularization algorithms for learning large incomplete matrices we use convex relaxation techniques to provide a sequence of regularized low rank solutions for large scale matrix completion problems using the nuclear norm as a regularizer we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm our algorithm soft impute iteratively replaces the missing elements with those obtained from a soft thresholded svd with warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter the computationally intensive part of our algorithm is in computing a low rank svd of a dense matrix exploiting the problem structure we show that the task can be performed with a complexity of order linear in the matrix dimensions our semidefinite programming algorithm is readily scalable to large matrices for example soft impute takes a few hours to compute low rank approximations of a 106 x 106 incomplete matrix with 107 observed entries and fits a rank 95 approximation to the full netflix training set in 3 3 hours our methods achieve good training and test errors and exhibit superior timings when compared to other competitive state of the art techniques

ranking of fuzzy sets based on the concept of existence abstract various approaches have been proposed for the comparison or ranking of fuzzy sets however due to the complexity of the problem a general method which can be used for any situation still does not exist this paper formalizes the concept of existence for the ranking of fuzzy sets many of the existing fuzzy ranking methods are shown to be some application of this concept an improved fuzzy ranking method is then introduced based on this concept this newly introduced method is expanded for treating both normal and nonnormal convex and nonconvex fuzzy sets emphasis is placed on the use of the subjectivity of the decision maker such as the optimistic or the pessimistic view points an improved procedure for obtaining linguistic conclusions is also developed finally some numerical examples are given to illustrate the approach

brief paper robust stability and h control of uncertain impulsive systems with time delay this paper investigates the problems of robust stability stabilization and h control for uncertain impulsive systems with time delay the parametric uncertainties are assumed to be time varying and norm bounded three classes of impulsive systems with time delay are considered the systems with stable stabilizable continuous dynamics and unstable unstabilizable discrete dynamics the systems with unstable unstabilizable continuous dynamics and stable stabilizable discrete dynamics and the systems where both the continuous time dynamics and the discrete time dynamics are stable stabilizable for each class of system by using the lyapunov function and razumikhin type techniques sufficient conditions for robust stability stabilization and h control are developed in terms of linear matrix inequalities numerical examples are given which illustrate the applicability of the theoretical results

stability analysis and design of impulsive control systems with time delay a class of impulsive control systems with time varying delays is considered by establishing an impulsive delay differential inequality we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate on the basis of the analysis a design procedure of impulsive controller is presented the designed impulsive controller not only can globally exponentially stabilize the time delay systems but also can control the exponential convergence rate of the systems two numerical examples are given to illustrate the effectiveness of the method

impulsive stabilization of a class of singular systems with time delays abstract this paper deals with the impulsive stabilization problem for a class of linear singular systems with time delays the stabilization is achieved by only exerting impulsive action on the slow state variables two novel lyapunov methods are presented to determine exponential stability of the impulsively controlled systems for the case where the time delay is unknown and may be time varying a lyapunov razumikhin method is developed in which the razumikhin condition is constructed by exploiting the relation among the fast state variables the slow state variables and their initial values for the case where the delay derivative is strictly less than 1 a descriptor type of impulse time dependent lyapunov functional is introduced which is discontinuous at impulse times but does not grow along the state trajectories by construction by using a convex technique the stability criteria are expressed in terms of linear matrix inequalities lmis then the impulsive controllers can be designed in the framework of lmis the effectiveness and advantages of the proposed methods are confirmed through simulation results

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

robust exponential input to state stability of impulsive systems with an application in micro grids abstract this paper studies the robust exponential input to state stability robust e iss for impulsive systems new notions of input to state exponent is e and e property are proposed based on the established relation between is e and e property and the method of variation of constants formula the equivalent conditions for robust e iss have been derived then the notion of robust event e iss is defined the sufficient conditions and the robust regions for robust e iss and robust event e iss are also derived by using the is e of every subsystem it shows the whole system may have robust event e iss while every subsystem may have no iss it also shows the external disturbances may lead to relatively small robust regions the results are then specialized to derive the equivalent conditions of interval e iss for interval impulsive systems as an application the result is used to test the iss for a controlled micro grid

random perturbation of low rank matrices improving classical bounds abstract matrix perturbation inequalities such as weyl s theorem concerning the singular values and the davis kahan theorem concerning the singular vectors play essential roles in quantitative science in particular these bounds have found application in data analysis as well as related areas of engineering and computer science in many situations the perturbation is assumed to be random and the original matrix has certain structural properties such as having low rank we show that in this scenario classical perturbation results such as weyl and davis kahan can be improved significantly we believe many of our new bounds are close to optimal and also discuss some applications

the two to infinity norm and singular subspace geometry with applications to high dimensional statistics the singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields myriad applications including clustering classification and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors this paper provides a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two to infinity norm motivated by preliminary deterministic procrustes analysis we consider a general matrix perturbation setting in which we derive a new procrustean matrix decomposition together with flexible machinery developed for the two to infinity norm this allows us to conduct a refined analysis of the induced perturbation geometry with respect to the underlying singular vectors even in the presence of singular value multiplicity our analysis yields singular vector entrywise perturbation bounds for a range of popular matrix noise models each of which has a meaningful associated statistical inference task in addition we demonstrate how the two to infinity norm is the preferred norm in certain statistical settings specific applications discussed in this paper include covariance estimation singular subspace recovery and multiple graph inference both our procrustean matrix decomposition and the technical machinery developed for the two to infinity norm may be of independent interest

extended fuzzy linear models and least squares estimates least squares regression of the fuzzy linear model is extended to overcome and interpret the occurrence of negative spreads 1 the idea is to introduce best fit difference models which exploit both the hukuhara difference and the l2 metric distance the fuzzy models use lr fuzzy numbers fitted models are compared by using the coefficient of determination in a similar way to its use in classical statistical least squares fitting the non lr fuzzy case is also considered

signal plus noise matrix models eigenvector deviations and fluctuations summary estimating eigenvectors and low dimensional subspaces is of central importance for numerous problems in statistics computer science and applied mathematics in this paper we characterize the behaviour of perturbed eigenvectors for a range of signal plus noise matrix models encountered instatistical and random matrix theoretic settings we establish both first order approximation results i e sharp deviations and second order distributional limit theory i e fluctuations the concise methodology presented in this paper synthesizes tools rooted in two core concepts namely deterministic decompositions of matrix perturbations and probabilistic matrix concentration phenomena we illustrate our theoretical results with simulation examples involving stochastic block model random graphs

a spectral technique for coloring random 3 colorable graphs let g3n p 3 be a random 3 colorable graph on a set of 3n vertices generated as follows first split the vertices arbitrarily into three equal color classes and then choose every pair of vertices of distinct color classes randomly and independently to be edges with probability p we describe a polynomial time algorithm that finds a proper 3 coloring of g3n p 3 with high probability whenever p geq c n where c is a sufficiently large absolute constant this settles a problem of blum and spencer who asked if an algorithm can be designed that works almost surely for p geq polylog n n j algorithms 19 1995 pp 204 234 the algorithm can be extended to produce optimal k colorings of random k colorable graphs in a similar model as well as in various related models implementation results show that the algorithm performs very well in practice even for moderate values of c

delayed impulsive control of takagi sugeno fuzzy delay systems in this paper the problem of exponential stability for takagi sugeno t s fuzzy delay systems with delayed impulses is addressed by means of the time dependent lyapunov function method combined with razumikhin technique a sufficient condition expressed in terms of linear matrix inequalities lmis is obtained for exponential stability of t s fuzzy delay systems with delayed impulses the derived stability condition depends both on the lower bound and the upper bound of impulsive intervals which is robust with respect to small impulse input delays by solving a set of lmis an impulsive state feedback controller can be easily constructed two numerical examples are discussed to illustrate the effectiveness of the theoretical findings

an algorithmic method to extend topsis for decision making problems with interval data in this paper from among multi criteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity ideal solution topsis approach has been dealt with in some cases determining precisely the exact value of the attributes is difficult and that as a result of this their values are considered as intervals therefore the aim of this paper is to extend the topsis method for decision making problems with interval data by extension of topsis method an algorithm to determine the most preferable choice among all possible choices when data is interval is presented finally an example is shown to highlight the procedure of the proposed algorithm at the end of this paper 2005 elsevier inc all rights reserved

stability of nonlinear differential systems with state dependent delayed impulses we consider nonlinear differential systems with state dependent delayed impulses impulses which involve the delayed state of the system for which the delay is state dependent such systems arise naturally from a number of applications and the stability issue is complex due to the state dependence of the delay we establish general and applicable results for uniform stability uniform asymptotic stability and exponential stability of the systems by using the impulsive control theory and some comparison arguments we show how restrictions on the change rates of states and impulses should be imposed to achieve system s stability in comparison with general impulsive delay differential systems with state dependent delay in the nonlinearity or the differential systems with constant delays in our approach the boundedness of the state dependent delay is not required but derives from the stability result obtained examples are given to demonstrate the sharpness and applicability of our general results and the proposed approach

matrix completion from noisy entries given a matrix m of low rank we consider the problem of reconstructing it from noisy observations of a small random subset of its entries the problem arises in a variety of applications from collaborative filtering the netflix problem to structure from motion and positioning we study a low complexity algorithm introduced by keshavan montanari and oh 2010 based on a combination of spectral techniques and manifold optimization that we call here optspace we prove performance guarantees that are order optimal in a number of circumstances

a note on exploratory item factor analysis by singular value decomposition we revisit a singular value decomposition svd algorithm given in chen et al psychometrika 84 124 146 2019b for exploratory item factor analysis ifa this algorithm estimates a multidimensional ifa model by svd and was used to obtain a starting point for joint maximum likelihood estimation in chen et al 2019b thanks to the analytic and computational properties of svd this algorithm guarantees a unique solution and has computational advantage over other exploratory ifa methods its computational advantage becomes significant when the numbers of respondents items and factors are all large this algorithm can be viewed as a generalization of principal component analysis to binary data in this note we provide the statistical underpinning of the algorithm in particular we show its statistical consistency under the same double asymptotic setting as in chen et al 2019b we also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory further extensions of the algorithm are discussed finally simulation studies suggest that the algorithm has good finite sample performance

matrix completion from a few entries let m be an n n matrix of rank r and assume that a uniformly random subset e of its entries is observed we describe an efficient algorithm which we call optspace that reconstructs m from e o rn observed entries with relative root mean square error 1 2 rmse c nr e 1 2 with probability larger than 1 1 n3 further if r o 1 and m is sufficiently unstructured then optspace reconstructs it exactly from e o n log n entries with probability larger than 1 1 n3 this settles in the case of bounded rank a question left open by candes and recht and improves over the guarantees for their reconstruction algorithm the complexity of our algorithm is o e r log n which opens the way to its use for massive data sets in the process of proving these statements we obtain a generalization of a celebrated result by friedman kahn szemeredi and feige ofek on the spectrum of sparse random matrices

recovering the missing components in a large noisy low rank matrix application to sfm in computer vision it is common to require operations on matrices with missing data for example because of occlusion or tracking failures in the structure from motion sfm problem such a problem can be tackled allowing the recovery of the missing values if the matrix should be of low rank when noise free the filling in of missing values is known as imputation imputation can also be applied in the various subspace techniques for face and shape classification online recommender systems and a wide variety of other applications however iterative imputation can lead to the recovery of data that is seriously in error in this paper we provide a method to recover the most reliable imputation in terms of deciding when the inclusion of extra rows or columns containing significant numbers of missing entries is likely to lead to poor recovery of the missing parts although the proposed approach can be equally applied to a wide range of imputation methods this paper addresses only the sfm problem the performance of the proposed method is compared with jacobs and shum s methods for sfm

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

sufficient stability conditions of nonlinear differential systems under impulsive control with state dependent delay in this technical note we study the delayed impulsive control of nonlinear differential systems where the impulsive control involves the delayed state of the system for which the delay is state dependent since the state dependence of the delay makes the impulsive transients dependent on the historical information of the states which means that it is hard to know exactly a priori how far in the history the information is needed the main challenge is how to determine the historical states we resolve this challenge and establish some sufficient conditions for local stability of nonlinear differential systems with state dependent delayed impulsive control based on impulsive control theory two examples are given to show the effectiveness of the proposed approach

stability and l2 gain analysis for impulsive delay systems an impulse time dependent discretized lyapunov functional method abstract the problems of exponential stability and l 2 gain for a class of time delay systems with impulsive effects are studied the main tool used is the construction of an impulse time dependent complete lyapunov functional by dividing the impulse interval and delay interval into several segments the matrix functions of this functional are chosen to be continuous piecewise linear moreover an impulse time dependent weighting factor is introduced to coordinate the dynamical behavior of the nondelayed and integral terms of this functional along the trajectories of the system by applying this functional delay dependent sufficient conditions for exponential stability and l 2 gain are derived in terms of linear matrix inequalities as by products new delay independent sufficient conditions for the same problems are also derived the efficiency of the proposed results is illustrated by numerical examples

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

brief paper input to state stability and integral input to state stability of nonlinear impulsive systems with delays this paper is concerned with analyzing input to state stability iss and integral iss iiss for nonlinear impulsive systems with delays razumikhin type theorems are established which guarantee iss iiss for delayed impulsive systems with external input affecting both the continuous dynamics and the discrete dynamics it is shown that when the delayed continuous dynamics are iss iiss but the discrete dynamics governing the impulses are not the iss iiss property of the impulsive system can be retained if the length of the impulsive interval is large enough conversely when the delayed continuous dynamics are not iss iiss but the discrete dynamics governing the impulses are the impulsive system can achieve iss iiss if the sum of the length of the impulsive interval and the time delay is small enough in particular when one of the delayed continuous dynamics and the discrete dynamics are iss iiss and the others are stable for the zero input the impulsive system can keep iss iiss no matter how often the impulses occur our proposed results are evaluated using two illustrative examples to show their effectiveness

further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects this paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time delay systems with delayed impulse effects by using the multiple lyapunov krasovskii functionals technique some exponential stability criteria are obtained respectively for two kinds of impulsive signals destabilizing impulsive signal and stabilizing impulsive signal the derived results not only characterise the effects of delayed impulse time delay and switching on nonlinear systems but also remove some restriction conditions furthermore a more precise bound of system state is given compared with existing results on related problems the obtained results are less conservative three examples are provided to illustrate the effectiveness and the generality of the proposed results

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

exponential stability of stochastic differential delay systems with delayed impulse effects in this paper we investigate the stability of stochastic delay differential systems with delayed impulses by razumikhin methods some criteria on the pth moment exponential stability are obtained it is shown that if a stochastic delay differential system is exponentially stable then under some conditions its stability is robust or weaken with respect to delayed impulses moreover it is also shown that an unstable stochastic delay system can be successfully stabilized by delayed impulses the effectiveness of the proposed results is illustrated by three examples

a new look at independence the concentration of measure phenomenon in product spaces is a farreaching abstract generalization of the classical exponential inequalities for sums of independent random variables we attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

laplacian eigenmaps from sparse noisy similarity measurements manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering but can be computationally expensive procedures when applied to large datasets or when similarities are expensive to compute to date little work has been done to investigate the tradeoff between computational resources and the quality of learned representations we present both theoretical and experimental explorations of this question in particular we consider laplacian eigenmaps embeddings based on a kernel matrix and explore how the embeddings behave when this kernel matrix is corrupted by occlusion and noise our main theoretical result shows that under modest noise and occlusion assumptions we can with high probability recover a good approximation to the laplacian eigenmaps embedding based on the uncorrupted kernel matrix our results also show how regularization can aid this approximation experimentally we explore the effects of noise and occlusion on laplacian eigenmaps embeddings of two real world datasets one from speech processing and one from neuroscience as well as a synthetic dataset

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

the power of convex relaxation near optimal matrix completion this paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries this is known as the matrix completion problem and comes up in a great number of applications including the famous netflix prize and other similar questions in collaborative filtering in general accurate recovery of a matrix from a small number of entries is impossible but the knowledge that the unknown matrix has low rank radically changes this premise making the search for solutions meaningful this paper presents optimality results quantifying the minimum number of entries needed to recover a matrix of rank r exactly by any method whatsoever the information theoretic limit more importantly the paper shows that under certain incoherence assumptions on the singular vectors of the matrix recovery is possible by solving a convenient convex program as soon as the number of entries is on the order of the information theoretic limit up to logarithmic factors this convex program simply finds among all matrices consistent with the observed entries that with minimum nuclear norm as an example we show that on the order of nr log n samples are needed to recover a random n x n matrix of rank r by any method and to be sure nuclear norm minimization succeeds as soon as the number of entries is of the form nr polylog n

effect of delayed impulses on input to state stability of nonlinear systems abstract this paper studies the input to state stability iss and integral input to state stability iiss of nonlinear systems with delayed impulses by using lyapunov method and the analysis technique proposed by hespanha et al 2005 some sufficient conditions ensuring iss iiss of the addressed systems are obtained those conditions establish the relationship between impulsive frequency and the time delay existing in impulses and reveal the effect of delayed impulses on iss iiss an example is provided to illustrate the efficiency of the obtained results

optimal fuzzy counterparts of scheduling rules the optimality of a fuzzy logic alternative to the usual treatment of uncertainties in a scheduling system using probability theory is examined formally fuzzy scheduling techniques proposed in the literature either fuzzify directly the existing scheduling rules or solve mathematical programming problems to determine the optimal schedules in the former method the fuzzy optimality for the optimal scheduling rules is usually not justified but still assumed in this paper the necessary conditions for fuzzy optimality are defined and fuzzy counterparts of some of the well known scheduling rules such as shortest processing time spt and earliest due date edd are developed

integral input to state stability for hybrid delayed systems with unstable continuous dynamics this paper considers integral input to state stability iiss for a class of hybrid time delay systems discrete dynamics includes impulsive and switching signals and continuous dynamics is not necessarily stable based on multiple lyapunov krasovskii functionals a dwell time bound is explicitly given to guarantee iiss of the hybrid delayed system compared with existing results on related problems the obtained stability criteria can be applied to a larger class of hybrid delayed systems moreover the obtained dwell time bound is less conservative than existing ones at last an example related to networked control systems ncss is provided to illustrate the effectiveness of the proposed result

the outliers of a deformed wigner matrix our results extend those of 21 by admitting overlapping outliers and by computing the joint distribution of all outliers in particular we give a complete description of the failure of universality first observed in 8 10 we also show that under suitable conditions outliers may be strongly correlated even if they are far from each other our proof relies on the isotropic local semicircle law established in 21 the main technical achievement of the current paper is the joint asymptotics of an arbitrary finite family of random variables of the form v h z 1w

optimal estimation and rank detection for sparse spiked covariance matrices this paper considers a sparse spiked covariance matrix model in the high dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection the optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established which requires significantly different techniques from those for estimating other structured covariance matrices such as bandable or sparse covariance matrices we also establish the minimax rate under the spectral norm for estimating the principal subspace the primary object of interest in principal component analysis in addition the optimal rate for the rank detection boundary is obtained this result also resolves the gap in a recent paper by berthet and rigollet ann stat 41 4 1780 1815 2013 where the special case of rank one is considered

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

stability of impulsive differential systems abstract this paper considers lyapunov stability of impulsive differential systems new sufficient conditions are derived which only require the lyapunov function to be nonincreasing along each subsequence of switching and to be bounded within two switching

exponential stability for impulsive delay differential equations by razumikhin method abstract in this paper we study exponential stability for impulsive delay differential equation of the form x t f t x t t t k x t i k t x t t t k k n by employing the razumikhin technique and lyapunov functions several exponential stability criteria are established some examples are also discussed to illustrate our results

comparison of fuzzy numbers using a fuzzy distance measure a new approach for ranking fuzzy numbers based on a distance measure is introduced a new class of distance measures for interval numbers that takes into account all the points in both intervals is developed first and then it is used to formulate the distance measure for fuzzy numbers the approach is illustrated by numerical examples showing that it overcomes several shortcomings such as the indiscriminative and counterintuitive behavior of several existing fuzzy ranking approaches

a riemannian optimization algorithm for joint maximum likelihood estimation of high dimensional exploratory item factor analysis there has been regained interest in joint maximum likelihood jml estimation of item factor analysis ifa recently primarily due to its efficiency in handling high dimensional data and numerous latent factors it has been established under mild assumptions that the jml estimator is consistent as both the numbers of respondents and items tend to infinity the current work presents an efficient riemannian optimization algorithm for jml estimation of exploratory ifa with dichotomous response data which takes advantage of the differential geometry of the fixed rank matrix manifold the proposed algorithm takes substantially less time to converge than a benchmark method that alternates between gradient ascent steps for person and item parameters the performance of the proposed algorithm in the recovery of latent dimensionality response probabilities item parameters and factor scores is evaluated via simulations

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

von neumann entropy penalization and low rank matrix estimation we study a problem of estimation of a hermitian nonnegatively definite matrix of unit trace for instance a density matrix of a quantum system based on n i i d measurements x1 y1 xn yn where

a general evidential reasoning algorithm for multi attribute decision analysis under interval uncertainty abstract evidential reasoning er is one of the important approaches used to solve multi attribute decision analysis mada problems under uncertainty involving both quantitative and qualitative attributes the er approach provides a distributed modeling framework fusing several types of uncertain and incomplete information including ignorance and vagueness to work out the optimum alternative rationally in this paper we review the original er algorithm and recursive interval evidential reasoning ier algorithm and derive a general analytical algorithm for ier thus enabling an aggregation of attributes assessments in an explicit manner then a more complicated uncertain occasion is investigated where it is possible to conduct evaluation assessments including quantitative data belief degrees grades and weights in the form of an interval a pair of nonlinear optimization models based on the new algorithm is established to solve this problem under interval uncertainty and the maximum and minimum expected utilities of each alternative are calculated and ranked accordingly additionally we prove that the original er and recursive ier algorithms are special cases of the new algorithm finally a numerical example is used to demonstrate the steps involved in the proposed approach

finite sample approximation results for principal component analysis a matrix perturbation approach principal component analysis pca is a standard tool for dimensional reduction of a set of n observations samples each with p variables in this paper using a matrix perturbation approach we study the nonasymptotic relation between the eigenvalues and eigenvectors of pca computed on a finite sample of size n and those of the limiting population pca as n oo as in machine learning we present a finite sample theorem which holds with high probability for the closeness between the leading eigenvalue and eigenvector of sample pca and population pca under a spiked covariance model in addition we also consider the relation between finite sample pca and the asymptotic results in the joint limit p n with p n c we present a matrix perturbation view of the phase transition phenomenon and a simple linear algebra based derivation of the eigenvalue and eigenvector overlap in this asymptotic limit moreover our analysis also applies for finite p n where we show that although there is no sharp phase transition as in the infinite case either as a function of noise level or as a function of sample size n the eigenvector of sample pca may exhibit a sharp loss of tracking suddenly losing its relation to the true eigenvector of the population pca matrix this occurs due to a crossover between the eigenvalue due to the signal and the largest eigenvalue due to noise whose eigenvector points in a random direction

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

lyapunov krasovskii functionals for switched nonlinear input delay systems under asynchronous switching this paper investigates the input to state stability for switched nonlinear input delay systems under asynchronous switching suppose a feedback control law has been designed such that the nominal closed loop system is exponentially stable for a certain switching signal and suppose further that a corresponding lyapunov function for the nominal closed loop system is available in the presence of input delay and asynchronous switching the system may not be stable under the same switching signal for this case we explicitly construct lyapunov krasovskii functionals based on the knowledge of the known lyapunov function then by using the constructed lyapunov krasovskii functionals a new switching delay dependent switching signal satisfying the new mode dependent average dwell time conditions is provided to guarantee the input to state stability of the system with respect to the disturbance under a certain input delay bound two examples are given to illustrate the effectiveness of the proposed theory

stabilization of linear systems with both input and state delays by observer predictors this paper studies the stabilization of linear systems with both state and input delays where the input delay can be arbitrarily large yet exactly known observer predictor based controllers are designed to predict the future states so that the input delay can be properly compensated necessary and sufficient conditions guaranteeing the stability of the closed loop system are provided in terms of the stability of some simple linear time delay systems refereed to as observer error systems by which the separation principle is discovered moreover approaches in terms of linear matrix inequalities are also provided to design both the state feedback gains and observer gains finally a numerical example illustrates that the proposed approaches are more effective and safe to implement than the existing methods

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis