robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

h filtering for fuzzy systems with immeasurable premise variables an uncertain system approach this paper discusses a design of stable filters with h disturbance attenuation of takagi sugeno fuzzy systems with immeasurable premise variables when we consider the filter design of takagi sugeno fuzzy systems the selection of premise variables plays an important role if the premise variable is the state of the system then a fuzzy system describes a wide class of nonlinear systems in this case however a filter design of fuzzy systems based on parallel distributed compensator idea is infeasible to avoid such a difficulty we consider the premise variables uncertainties then we consider a robust h filtering problem for such an uncertain system a solution of the problem is given in terms of linear matrix inequalities lmis some numerical examples are given to illustrate our theory

rank revealing qr factorizations abstract an algorithm is presented for computing a column permutation pi and a qr factorization a pi qr of an m by n m or n matrix a such that a possible rank deficiency of a will be revealed in the triangular factor r having a small lower right block for low rank deficient matrices the algorithm is guaranteed to reveal the rank of a and the cost is only slightly more than the cost of one regular qr factorization a posteriori upper and lower bounds on the singular values of a are derived and can be used to infer the numerical rank of a keywords qr factorization rank deficient matrices least squares computation subset selection rank singular values

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

robust h filtering for sampled data fuzzy systems abstract this paper is concerned with robust h filtering for takagi sugeno sampled data fuzzy systems with uncertain parameters takagi sugeno fuzzy system can describe a wide class of nonlinear systems and is widely used in many engineering fields recently system analysis and control design for nonlinear systems based fuzzy system approach have been active the system is usually modelled as a continuous time system while in practical situations the observation is taken at discrete instants such an observation can be represented as a delayed signal first it is shown that the error system which stems from an original fuzzy system and a sampled data filter becomes a system with time varying delay sufficient conditions for the error system to achieve the robust stability with h disturbance attenuation are given in terms of linear matrix inequalities lmis we derive such conditions via output delay system approach under the assumption that sampling time is not greater than some prescribed number based on such conditions we propose a robust h sampled data filter design for a fuzzy system we consider two different cases for the premise variables in our filter design numerical examples are given to illustrate our robust h sampled data filtering

the discrimination subspace model abstract for a p variate normal random vector measured in two populations we propose a method of discrimination under the constraint that all differences between the two populations occur in a subspace of dimension q p this method of classification is based on the discrimination subspace model denoted by dsm q and is intermediate between linear and quadratic discrimination it combines the ideas of dimension reduction and constraints on the parameter space thus substantially reducing the number of parameters to be estimated the maximum likelihood estimators of the model are presented and the performance of dsm q versus quadratic and linear discrimination is assessed via simulation it is generally shown that discrimination based on dsm q consistently yields noticeably lower expected actual error rates relative to the traditional methods the method is illustrated with a real data example and is compared to linear and quadratic discrimination using a leave one out method the example confirms t

simultaneous detection of shift in means and variances abstract suppose that x is a p variate random vector measured in two populations with mean vector j and covariance matrix j in population j j 1 2 in this article we study normal theory estimation of the parameters under the following constraints it is assumed that a the covariance matrices have p identical eigenvectors b in the coordinate system given by the common eigenvectors only q p of the means are different between groups and c only the q eigenvalues associated with the same q common eigenvectors are different between groups there are two main areas of application of these models a in morphometric studies particularly if size differences between groups are to be removed from the analysis and b in testing for equality of mean vectors and covariance matrices especially in situations where the number of variables p is large for applications of type b we suggest a randomization test and compare its performance to the t 2 test and to the likelihood ratio test for equali

partial singular value decomposition algorithm algorithm 32 abstract the partial singular value decomposition psvd subroutine computes a basis of the left and or right singular subspace of a matrix corresponding to its smallest singular values the dimension of the desired subspace may be fixed or depend on a given upper bound for those smallest singular values as only a basis of the desired singular subspace is needed the classical singular value decomposition svd algorithm is modified in three ways first the householder transformations of the bidiagonalization are only applied to the base vectors of the desired singular subspace second the bidiagonal is only partially diagonalized and third the convergence rate of the iterative diagonalization is improved by an appropriate choice between qr and ql iteration steps depending on the gap the desired numerical accuracy and the dimension of the desired subspace psvd can be three times faster than the classical svd algorithm while the same accuracy can be maintained the new algorithm can be successfully used in total least squares applications in the computation of the null space of a matrix an in solving non homogeneous linear equations

sampled data h fuzzy filtering for nonlinear systems with missing measurements in this paper a sampled data h fuzzy filtering problem is considered for nonlinear systems with missing measurements the nonlinear sampled data system and missing measurements are assumed to be represented by a takagisugeno ts fuzzy system and an independent identically distributed bernoulli random process respectively based on the fuzzy system the h fuzzy filtering problem is formulated to design the sampled data fuzzy filter by using the exponential mean square stability definition the stability condition with an h performance is guaranteed for the fuzzy system with the sampled data fuzzy filter and its sufficient condition is converted into the linear matrix inequality lmi format finally an example is provided to verify the effectiveness of the proposed fuzzy filtering technique

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

regularized gaussian discriminant analysis through eigenvalue decomposition abstract friedman proposed a regularization technique rda of discriminant analysis in the gaussian framework rda uses two regularization parameters to design an intermediate classifier between the linear the quadratic the nearest means classifiers in this article we propose an alternative approach called edda that is based on the reparameterization of the covariance matrix k of a group gk in terms of its eigenvalue decomposition k k d k a k d k where k specifies the volume of density contours of gk the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation variations on constraints concerning volumes shapes orientations k a k and d k lead to 14 discrimination models of interest for each model we derived the normal theory maximum likelihood parameter estimates our approach consists of selecting a model by minimizing the sample based estimate of future misclassification risk by cross validation numerical experiments on simulated and rea

decentralized dynamic output feedback control for affine fuzzy large scale systems with measurement errors this paper investigates the decentralized output feedback control problem for affine fuzzy large scale systems with unknown interconnections a decentralized piecewise dynamic output feedback controller is constructed and the measurement errors between actual outputs and measured outputs are considered in control synthesis by introducing the s procedure and a cyclic small gain condition novel controller design conditions in terms of linear matrix inequalities lmis are derived which allow for reducing the worst case peak output due to measurement errors with satisfying an l norm constraint finally two examples are given to illustrate the effectiveness and superiority of the new results

a fast algorithm for index of annihilation computations in this paper a fast algorithm for computing the index of annihilation of the associated pencil of a given matrix is presented knowledge of this index leads us to the specification of the elementary divisors of the matrix and thus we can specify its canonical forms it is shown that the new algorithm which is based on the rrqr decomposition is faster than the existing svd approach the algorithm can be also applied to matrix pencils and thus specify the structure of their elementary divisors

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

decentralized sampled data fuzzy observer design for nonlinear interconnected systems this paper presents the decentralized sampled data fuzzy observer design techniques for nonlinear interconnected systems which are assumed to be composed of fuzzy subsystems and unknown interconnections to design the decentralized fuzzy observer the estimation error dynamics is obtained and the performance function is defined based on the estimation error dynamics and the performance function the continuous time decentralized fuzzy observer is first proposed to minimize the interconnection bound to attenuation degree ratio in addition the decentralized sampled data fuzzy observers are designed by using the approximate discretization and the exact discrete time design approaches respectively each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities finally several simulation examples show the validity and superiority of the proposed observer design techniques by comparing with the conventional techniques

high performance algorithms for toeplitz and block toeplitz matrices in this paper we present several high performance variants of the classical schur algorithm to factor various toeplitz matrices for positive definite block toeplitz matrices we show how hyperbolic householder transformations may be blocked to yield a block schur algorithm this algorithm uses blas3 primitives and makes efficient use of a memory hierarchy we present three algorithms for indefinite toeplitz matrices two of these are based on look ahead strategies and produce an exact factorization of the toeplitz matrix the third produces an inexact factorization via perturbations of singular principal miners we also present an analysis of the numerical behavior of the third algorithm and derive a bound for the number of iterations to improve the accuracy of the solution for rank deficient toeplitz least squares problems we present a variant of the generalized schur algorithm that avoids breakdown due to an exact rank deficiency in the presence of a near rank deficiency an approximate rank factorization of the toeplitz matrix is produced finally we suggest an algorithm to solve the normal equations resulting from a real toeplitz least squares problem based on transforming to cauchy like matrices this algorithm exploits both realness and symmetry in the normal equations

an efficient and reliable algorithm for computing the singular subspace of a matrix associated with its smallest singular values abstract in this paper an improved algorithm psvd for computing the singular subspace of a matrix corresponding to its smallest singular values is presented as only a basis of the desired singular subspace is needed the classical singular value decomposition svd algorithm can be modified in three ways first the householder transformations of the bidiagonalization need only to be applied on the base vectors of the desired singular subspace second the bidiagonal must only be partially diagonalized and third the convergence rate of the iterative diagonalization can be improved by an appropriate choice between qr and ql iteration steps an analysis of the operation counts as well as computational results show the relative efficiency of psvd with respect to the classical svd algorithm depending on the gap the desired numerical accuracy and the dimension of the desired subspace psvd can be three times faster than the classical svd algorithm while the same accuracy can be maintained the new algorithm can be successfully used in total least squares applications in the computation of the null space of a matrix and in solving non homogeneous linear equations based on psvd a very efficient and reliable algorithm is also derived for solving nonhomogeneous equations

decentralized h fuzzy filter for nonlinear large scale sampled data systems with uncertain interconnections abstract this paper proposes a decentralized h fuzzy filter technique for nonlinear large scale interconnected systems that are based on the takagi sugeno fuzzy model the large scale system has unknown interconnection terms that are assumed to satisfy the quadratic bounds an error system between the nonlinear large scale system and the decentralized filter is constructed by using the fuzzy lyapunov technique sufficient conditions are proposed for both showing asymptotic stability and guaranteeing h fuzzy filter performance these sufficient conditions are derived in terms of linear matrix inequalities finally simulation examples are given to demonstrate the effectiveness of the proposed technique

using gauss jordan elimination to compute the index generalized nullspaces and drazin inverse abstract we develop and analyze a new algorithm that computes bases for the null spaces of all powers of a given matrix as well as its index the algorithm uses row operations and shuffling steps in which rows of pairs of matrices are interchanged in particular the new algorithm may be viewed as an extension of the classic gauss jordan elimination method for inverting a nonsingular matrix it is also shown that the drazin inverse has a simple representation in terms of the output of the algorithm and the original matrix

sampled data filtering of takagi sugeno fuzzy neural networks with interval time varying delays abstract this paper is concerned with sample data filtering of t s fuzzy neural networks with interval time varying delays which is formed by a fuzzy plant with time delay and a sampled data fuzzy controller connected in a closed loop a takagi sugeno t s fuzzy model is adopted for the neural networks and the sampled data fuzzy controller is designed for a t s fuzzy system to develop the guaranteed cost control a new stability condition of the closed loop system is guaranteed in the continuous time lyapunov sense and its sufficient conditions are formulated in terms of linear matrix inequalities by using a descriptor representation the sampled data fuzzy control system with time delay can be reduced to ease the stability analysis which effectively leads to a smaller number of lmi stability conditions information of the membership functions of both the fuzzy plant model and fuzzy controller are considered which allows arbitrary matrices to be introduced to ease the satisfaction of the stability conditions by a newly proposed inequality bounding technique the fuzzy sampled data filtering performance analysis is carried out such that the resultant neural networks is asymptotically stable numerical example and simulation result are given to illustrate the usefulness and effectiveness of the proposed theoretical results

error rates of non bayes classification rules and the robustness of fisher s linear discriminant function summary we call a classification procedure non bayes if it does not converge to the bayes classification procedure an asymptotic expansion is found for the expected error rate of such a classification rule this is used to compare the estimates of fisher s linear discriminant rule f and the quadratic discriminant rule q under departures from the equal variance matrices assumption it is found that f is quite robust to departures from the equal variances assumption

event triggered fuzzy control for nonlinear networked control systems abstract this paper investigates the problem of event triggered et dynamic output feedback controller dofc design for nonlinear networked control systems ncss in the framework of interval type 2 it2 fuzzy systems the parameter uncertainties in the nonlinear plant can be captured effectively by utilizing the membership functions with upper and lower bounds to reduce the utilization of limited network bandwidth an et communication mechanism is applied a novel type of dofc subject to parameter uncertainties et communication mechanism and transmission delay is proposed where the membership functions are different from those of the fuzzy models consequently the closed loop system is with mismatched membership functions which hampers the stability analysis and controller design to promote the stability analysis and achieve a better control performance the information of membership functions and slack matrices are utilized for obtaining the main results finally a simulation example is employed to demonstrate the effectiveness of the proposed mechanism

on the computation of the rank of block bidiagonal toeplitz matrices in the present paper we study the computation of the rank of a block bidiagonal toeplitz bbt sequence of matrices we propose matrix based numerical and symbolical updating and direct methods computing the rank of bbt matrices and comparing them with classical procedures the methods deploy the special form of the bbt sequence significantly reducing the required flops and leading to fast and efficient algorithms the numerical implementation of the algorithms computes the numerical rank in contrast with the symbolical implementation which guarantees the computation of the exact rank of the matrix the combination of numerical and symbolical operations suggests a new approach in software mathematical computations denoted as hybrid computations

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

penalized discriminant analysis fisher s linear discriminant analysis lda is a popular data analytic tool for studying the relationship between a set of predictors and a categorical response in this paper we describe a penalized version of lda it is designed for situations in which there are many highly correlated predictors such as those obtained by discretizing a function or the grey scale values of the pixels in a series of images in cases such as these it is natural efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients both for improved prediction performance and interpretability we cast the classification problem into a regression framework via optimal scoring using this our proposal facilitates the use of any penalized regression technique in the classification setting the technique is illustrated with examples in speech recognition and handwritten character recognition

an improved digital redesign for sampled data fuzzy control systems this paper proposes an improved digital redesign dr technique for sampled data fuzzy controllers in nonlinear systems based on a takagisugeno ts fuzzy model to improve the performance of the dr technique two methodologies are used a state matching error cost function and a continuous time fuzzy lyapunov function using these two methodologies a novel dr technique is proposed to guarantee both the stability and state matching conditions of the sampled data fuzzy control system further the proposed dr technique is represented as an optimal problem using the linear matrix inequality lmi format finally some simulation examples are provided to verify the effectiveness of the proposed technique in comparison with previous techniques

decentralized h_ infty filter design for discrete time interconnected fuzzy systems this paper describes a decentralized h infin filter design for discrete time interconnected fuzzy systems based on piecewise quadratic lyapunov functions the systems consist of j discrete time interconnected takagi sugeno t s fuzzy subsystems and a decentralized h infin filter is designed for each subsystem it is shown that the stability of the overall filtering error system with h infin performance can be established if a piecewise quadratic lyapunov function can be constructed moreover the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible two simulation examples are given to show the effectiveness of the proposed approach