robust static output feedback stabilization for nonlinear discrete time systems with time delay via fuzzy control approach this paper addresses the problem of designing robust static output feedback controllers for nonlinear discrete time interval systems with time delays both in states and in control input in the approach we do not directly employ the lyapunov approach as do in most of traditional fuzzy control design approaches instead sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed loop fuzzy system the stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the matlab linear matrix inequality lmi toolbox finally an example is provided to illustrate the effectiveness of the proposed approach

on the stability of fuzzy systems studies the global asymptotic stability of a class of fuzzy systems it demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant lti switching systems a necessary and sufficient condition for the stability of such systems are given and it is shown that under the sufficient condition a common lyapunov function exists for the lti subsystems a particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic lyapunov function a constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

approximation by kantorovich form of modified szszmirakyan operators in the present article we consider the kantorovich type generalized szszmirakyan operators based on jain and pethe operators 32 we study local approximation results in terms of classical modulus of continuity as well as ditziantotik moduli of smoothness further we establish the rate of convergence in class of absolutely continuous functions having a derivative coinciding a e with a function of bounded variation

estimation in linear models with censored data summary three methods for linear regression with censored data are considered that of buckley james 1979 a proposed simpler nonparametric method and a normal model for censored data a new estimator for the variance of the error term in buckley james s 1979 procedure is proposed and simulations comparing the three methods are described many methods have been proposed for handling regression problems in which the dependent variable may be censored we focus on three methods for the linear model y xt3 e two methods are nonparametric so that the distribution of e is unspecified while the third assumes that e is normally distributed the nonparametric methods are analogous to the expectation maximization em algorithm introduced by dempster laird rubin 1977 which is broadly applicable for computing maximum likelihood estimates in 2 we discuss each of these methods and propose a new estimator of the variance of e for the buckley james method in 3 we give simulation results which compare the three methods

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

a multirule base controller using the robust property of a fuzzy controller and its design method this paper suggests a new fuzzy adaptive controller which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers it explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller the basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers this new adaptive controller uses a multirule base architecture which has several independent fuzzy controllers in parallel each with different robust stability area out of several independent fuzzy controllers the most suited one is selected by a system identifier which observes variations in the controlled system parameter here we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system related mathematical theorems and their proofs are also given the performance of the proposed adaptive control algorithm is analyzed through a design example and a dc motor control simulation

robust stabilization of the takagi sugeno fuzzy model via bilinear matrix inequalities quadratic stability has enabled mainly via the linear matrix inequality framework the analysis and design of a nonlinear control system from the local matrices of the system s takagi sugeno t s fuzzy model it is well known however that there exist stable differential inclusions hence t s fuzzy models whose stability is unprovable by a globally quadratic lyapunov function at present literature in the broader area of stability analysis suggests piecewise quadratic stability as a means to avoid such conservatism this paper generalizes the idea and proposes a framework that supports less conservative sufficient conditions for the stability of the t s model by using piecewise quadratic generalized lyapunov functions the advocated approach results in the formulation of the controller synthesis which herein aims for robust stabilization as a problem of bilinear rather than linear matrix inequalities simulation studies which include an algorithm for solution of bilinear matrix inequalities demonstrate the proposed method

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

improved approximation and error estimations by king type p q szasz mirakjan kantorovich operators abstract in the present paper two different modifications are proposed for p q szasz mirakjan kantorovich operators which preserve some test functions some approximation results with the help of better known korovkin s theorem and weighted korovkin s theorem for these operators are presented furthermore convergence properties in terms of modulus of continuity and class of lipschitz functions are studied it has been shown that for a given absolute error bound king type modified p q szasz mirakjan kantorovich operators require lesser value of m and elapsed time within some subintervals further for comparisons some graphics and error estimation tables are presented using matlab r2018a

on simultaneously nilpotent fuzzy matrices abstract nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices in this paper we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices the notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix properties of the simultaneous nilpotence will be established in the study of consecutive powers of a fuzzy matrix a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix in this paper we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices similar to the nilpotent characterization for a controllable fuzzy matrix the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

a pseudo r2 measure for limited and qualitative dependent variable models abstract a pseudo r 2 measure for limited and qualitative dependent variable models is proposed a consistent estimator of the variance of the disturbance term is also suggested the pseudo r 2 measure is shown to have the same asymptotic limit as the conventional r 2 the measure is adapted to the logit model in an empirical example of female car ownership modeling the pseudo r 2 is applicable to a wide set of limited and qualitative dependent variable models and offers a valuable tool for model evaluation

sampling theory for not necessarily band limited functions a historical overview shannon s sampling theorem is one of the most powerful results in signal analysis the aim of this overview is to show that one of its roots is a basic paper of de la vallee poussin of 1908 the historical development of sampling theory from 1908 to the present especially the matter dealing with not necessarily band limited functions which includes the duration limited case actually studied in 1908 is sketched emphasis is put on the study of error estimates as well as on the delicate point wise behavior of sampling sums at discontinuity points of the signal to be reconstructed

stable adaptive control of fuzzy dynamic systems this paper discusses fuzzy model reference adaptive control for a class of nonlinear systems the system concerned is represented by a family of local transfer function models smoothly connected together by fuzzy membership functions the model reference adaptive control law is first designed in each local region and then constructed in global domain it is shown that the resulting fuzzy adaptive control system is globally stable based on a suitable piecewise differentiable lyapunov function a simulation example is given for demonstration of the application of the method

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

an r squared measure of goodness of fit for some common nonlinear regression models abstract for regression models other than the linear model r squared type goodness of fit summary statistics have been constructed for particular models using a variety of methods we propose an r squared measure of goodness of fit for the class of exponential family regression models which includes logit probit poisson geometric gamma and exponential this r squared is defined as the proportionate reduction in uncertainty measured by kullback leibler divergence due to the inclusion of regressors under further conditions concerning the conditional mean function it can also be interpreted as the fraction of uncertainty explained by the fitted model

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

continuity of the generalized spectral radius in max algebra abstract let be an induced matrix norm associated with a monotone norm on r n and be the collection of all nonempty closed and bounded subsets of n n nonnegative matrices under this matrix norm for the hausdorff metric h between and is given by h max sup a inf b a b sup b inf a a b the max algebra system consists of the set of nonnegative numbers with sum a b max a b and the standard product ab for a b 0 for n n nonnegative matrices a b their product is denoted by a b where a b ij max 1 k n a ik b kj for each the max algebra version of the generalized spectral radius of is limsup m sup a m a 1 m where m a 1 a 2 a m a i here a is the maximum circuit geometric mean in this paper we prove that the max algebra version of the generalized spectral radius is continuous on the hausdorff metric space h the notion of the max algebra version of simultaneous nilpotence of matrices is also proposed necessary and sufficient conditions for the max algebra version of simultaneous nilpotence of matrices are presented as well

on the convergence of powers of interval matrices abstract we give a necessary and sufficient condition for the sequence a k of the powers of an interval matrix a to converge to the null matrix o we construct a point matrix b which has spectral radius b less than one if a k converges

interpolation by neural network operators activated by ramp functions abstract in this paper a family of interpolation neural network operators are introduced here ramp functions as well as sigmoidal functions generated by central b splines are considered as activation functions the interpolation properties of these operators are proved together with a uniform approximation theorem with order for continuous functions defined on bounded intervals the relations with the theory of neural networks and with the theory of the generalized sampling operators are discussed

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

sufficient conditions for the stability of linear takagi sugeno free fuzzy systems in this paper we will study the stability issues of the linear takagi sugeno t s free fuzzy systems based on matrix norm we propose a new sufficient condition for the linear t s free fuzzy system to be globally asymptotically stable we then study the stability analysis in the case of systems with consequent parameter uncertainty based on mayer s convergent theorem we propose a sufficient condition which is easily implemented for the systems with consequent parameter uncertainty to be globally asymptotically stable

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

approximation by periodic multivariate quasi projection operators abstract approximation properties of periodic quasi projection operators with matrix dilations are studied such operators are generated by a sequence of functions j and a sequence of distributions functions j error estimates for sampling type quasi projection operators are obtained under the periodic strang fix conditions for j and the compatibility conditions for j and j these estimates are given in terms of the fourier coefficients of approximated functions and provide analogs of some known non periodic results under some additional assumptions error estimates are given in other terms in particular using the best approximation a number of examples are provided

dyadic calculus and sampling theorems for functions with multidimensional domain ii applications to dyadic sampling representations part ii is concerned with applications of the general theory of multidimensional dyadic analysis to dyadic sampling theorems for various types of signals together with rates of approximation and orders of magnitude for the aliasing error respectively the theory developed in part i the contents of which are assumed to be known here is now applied in order to study various types of sampling theorems it may be mentioned that there does not exist any paper at all dealing with multidimensional dyadic sampling theorems this can for example be seen in the survey paper by a j jerri 1977 proc inst electr engrs 65 1565 1596 nevertheless in the classical multidimensional fourier case there are some papers dealing with sampling representations for functions of several variables see e g prosser 1966 petersen and middleton 1962 and miyakawa 1959

quasi projection operators with applications to differential difference expansions abstract a large class of multivariate quasi projection operators is studied these operators are sampling type expansions k z d c k f a j k where a is a matrix and the coefficients ck f are associated with a tempered distribution error estimates in lp norm 2 p and and the strang fix conditions for approximation order depends on the smoothness of f and on the order of the compatibility and the strang fix conditions a number of examples aimed at engineering applications are provided a special attention is payed to the quasi projection operators associated with differential difference expansions applications to solving some differential difference equations are presented

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

approximation error of the whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals the whittaker shannon kotel nikov sampling theorem enables one to reconstruct signals f bandlimited to w w from its sampled values f k w k z in terms of swf t k f kw sinc wt k f t t r if f is continuous but not bandlimited one normally considers limw swf t in the supremum norm together with aliasing error estimates expressed in terms of the modulus of continuity of f or its derivatives since in practice signals are however often discontinuous this paper is concerned with the convergence of swf to f in the lp r norm for 1 p the classical modulus of continuity being replaced by the averaged modulus of smoothness r f w 1 m r p the major theorem enables one to sample any bounded signal f belonging to a certain subspace p of lp r the jump discontinuities of which may even form a set of measure zero on r a corollary gives the counterpart of the approximate sampling theorem now in the lp norm the averaged modulus so far only studied for functions defined on a compact interval a b had first to be extended to functions defined on the whole real axis r basic tools are the de la vallee poussin means and a semi discrete hilbert transform

stability analysis and synthesis for an affine fuzzy control system via lmi and ilmi a continuous case a new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper the method suggested is based on the numerical convex optimization techniques in analysis the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities lmis the emphasis of this paper however is on the synthesis of fuzzy controller based on the derived stability condition in the synthesis the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains continuous iterative lmi ilmi approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system

the finiteness conjecture for the generalized spectral radius of a set of matrices the generalized spectral radius g9 of a set of n n matrices is g9 lim supk g9k 1k where g9k sup a1a2 ak each ai the joint spectral radius g9 is g9 lim supk g9k 1k where g9k sup a1 ak each ai it is known that g9 g9 holds for any finite set of n n matrices the finiteness conjecture asserts that for any finite set of real n n matrices there exists a finite k such that g9 g9 g9k 1k the normed finiteness conjecture for a given operator norm asserts that for any finite set a1 am having all ai op 1 either g9 1 or g9 g9 g9k 1k 1 for some finite k it is shown that the finiteness conjecture is true if and only if the normed finiteness conjecture is true for all operator norms the normed finiteness conjecture is proved for a large class of operator norms extending results of gurvits in particular for polytope norms and for the euclidean norm explicit upper bounds are given for the least k having g9 g9k 1k these results imply upper bounds for generalized critical exponents for these norms

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

approximation of discontinuous signals by sampling kantorovich series abstract in this paper the behavior of the sampling kantorovich operators has been studied when discontinuous functions signals are considered in the above sampling series moreover the rate of approximation for the family of the above operators is estimated when uniformly continuous and bounded signals are considered finally several examples of duration limited kernels which satisfy the assumptions of the present theory have been provided and also the problem of the linear prediction by sampling values from the past is analyzed

on the stability of takagi sugeno fuzzy systems with time varying uncertainties this paper studies the problems of stability analysis of takagi sugeno free fuzzy systems with time varying uncertainties in our prior study we represented the time varying uncertainty incurred in characteristic interval matrices in terms of the stability of takagi sugeno free fuzzy systems with consequent parameter uncertainties based on mayer s convergent theorem for powers of single interval matrix and its generalization we further proposed some sufficient conditions for the takagi sugeno free fuzzy system with time varying uncertainties to be globally asymptotically stable in this paper we propose the notion of simultaneously nilpotent interval matrices to investigate the takagi sugeno free fuzzy system with time varying uncertainties to be strongly stable within steps where relates to the dimension of interval matrices moreover a unique situation for the deterministic takagi sugeno free fuzzy system to be strongly stable within steps is derived as well where relates to the dimension of characteristic matrices for the deterministic takagi sugeno free fuzzy system

on the asymptotic bias of the ordinary least squares estimator of the tobit model this paper presents a precise characterization of the bias of least squares in two limited dependent variable models the tobit model and the truncated regression model for the cases considered the method of moments can be used to correct the bias of ols for more general cases the results provide approximations which appear to be relatively robust 13 and o in this paper we present a precise characterization of that bias for the particular case in which xt as well as is normally distributed we also show that the bias of the ols slope estimator can be corrected by dividing each estimate by the sample proportion of nonlimit observations other structural parameters can be consistently estimated in a similar fashion we present some evidence on the effect of nonnormality with respect to the predictions obtained in the normal model the case in which the sample contains only nonlimit observation the truncated regression model is considered elsewhere olsen 7 we analyze the relationship between his results and ours and derive some predictions of the normal model with respect to the seriousness of truncation bias

vitali type theorems for filter convergence related to vector lattice valued modulars and applications to stochastic processes a vitali type theorem for vector lattice valued modulars with respect to filter convergence is proved some applications are given to modular convergence theorems for moment operators in the vector lattice setting and also for the brownian motion and related stochastic processes

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

a comparison between the sampling kantorovich algorithm for digital image processing with some interpolation and quasi interpolation methods abstract in this paper we study the performance of the sampling kantorovich s k algorithm for image processing with other well known interpolation and quasi interpolation methods the s k algorithm has been implemented with three different families of kernels central b splines jackson type and bochner riesz the above method is compared in term of psnr peak signal to noise ratio and cpu time with the bilinear and bicubic interpolation the quasi fir finite impulse response and quasi iir infinite impulse response approximation experimental results show better performance of s k algorithm than the considered other ones

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

the max product generalized sampling operators convergence and quantitative estimates abstract in this paper we study the max product version of the generalized sampling operators based upon a general kernel function in particular we prove pointwise and uniform convergence for the above operators together with a certain quantitative jackson type estimate based on the first order modulus of continuity of the function being approximated the proof of the proposed results are based on the definition of the so called generalized absolute moments by the proposed approach the achieved approximation results can be applied for several type of kernels not necessarily duration limited such as the sinc function the fejer kernel and many others examples of kernels with compact support for which the above theory holds can be given for example by the well known central b splines

robust controllability of t s fuzzy model based control systems with parametric uncertainties the robust controllability problem for the takagi sugeno t s fuzzy model based control systems is studied in this paper under the assumption that the nominal t s fuzzy model based control systems are locally controllable i e each fuzzy rule of the nominal t s fuzzy model based control systems has a full row rank for its controllability matrix a sufficient condition is proposed to preserve the assumed property when the parameter uncertainties are added into the nominal t s fuzzy model based control systems the proposed sufficient condition can provide the explicit relationship of the bounds on parameter uncertainties to preserve the assumed property besides a robustly global controllability condition and the related robustly global stabilizability condition of the uncertain t s fuzzy model based control systems are also presented in this paper a nonlinear mass spring damper mechanical system with parameter uncertainties is given as an example to illustrate the application of the proposed sufficient conditions

detection of thermal bridges from thermographic images by means of image processing approximation algorithms in this paper we develop a procedure for the detection of the contours of thermal bridges from thermographic images in order to study the energy performance of buildings two main steps of the above method are the enhancement of the thermographic images by an optimized version of the mathematical algorithm for digital image processing based on the theory of sampling kantorovich operators and the application of a suitable thresholding based on the analysis of the histogram of the enhanced thermographic images finally an improvement of the parameter defining the thermal bridge is obtained

the approximation operators with sigmoidal functions the aim of this paper is to investigate the error which results from the method of approximation operators with logarithmic sigmoidal function by means of the method of extending functions a class of feed forward neural network operators is introduced using these operators as approximation tools the upper bounds of errors in uniform norm approximating continuous functions are estimated also a class of quasi interpolation operators with logarithmic sigmoidal function is constructed for approximating continuous functions defined on the total real axis

prediction by samples from the past with error estimates covering discontinuous signals there are several reasons why the classical sampling theorem is rather impractical for real life signal processing first the sinc kernel is not very suitable for fast and efficient computation it decays much too slowly second in practice only a finite number n of sampled values are available so that the representation of a signal f by the finite sum would entail a truncation error which decreases rather slowly for n due to the first drawback third band limitation is a definite restriction due to the nonconformity of band and time limited signals further the samples needed extend from the entire past to the full future relative to some time t t0 this paper presents an approach to overcome these difficulties the sinc function is replaced by certain simple linear combinations of shifted b splines only a finite number of samples from the past need be available this deterministic approach can be used to process arbitrary not necessarily bandlimited nor differentiable signals and even not necessarily continuous signals best possible error estimates in terms of an lp average modulus of smoothness are presented several typical examples exhibiting the various problems involved are worked out in detail

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

measures of dependence for censored survival data in the linear regression model with normal errors the squared product moment correlation provides the standard measure of dependence between the explanatory variable and the response variable using the concept of information gain a measure of dependence can also be defined for more general regression models used in survival analysis such as the weibull regression model or cox s proportional hazards model further this measure of dependence can be conveniently estimated even when the response variable is subject to censoring and a simple approximation is available

an approach to adaptive control of fuzzy dynamic systems this paper discusses adaptive control for a class of fuzzy dynamic models the adaptive control law is first designed in each local region and then constructed in the global domain it is shown that the resulting fuzzy adaptive control system is globally stable robustness issues of the adaptive control system are also addressed a simulation example is given for demonstration of the application of the approach

sampling approximation of continuous functions with multidimensional domain corresp after evaluating shannon s sampling theorem for functions of several variables the aliasing error is estimated in dependence upon smoothness conditions as a main tool the concept of multidimensional convolution integrals is introduced in particular those of de la vallee poussin which are also helpful in constructing generalized sampling series having better aliasing bounds

asymptotic stability and generalized gelfand spectral radius formula let be a set of n n complex matrices for m 1 2 let m be the set of all products of matrices in of length m denote by the multiplicative semigroup generated by is said to be asymptotically stable in the sense of dynamical systems if there is 0 1 such that there are bounded neighborhoods u v cn of the origin for which av mu for all a m m 1 2 for a bounded set of n n complex matrices it is shown that the following conditions are mutually equivalent i is asymptotically stable ii g9 lim supm supa m a 1 m 1 iii lim supm supa m a 1 m 1 where a stands for the spectral radius of a and iv there exists a positive number such that a 1 for all a this fact answers an open question raised by brayton and tong the generalized gelfand spectral radius formula that is g9 conjectured by daubechies and lagarias and proved by berger and wang using advanced tools from ring theory and then by elsner using analytic geometric tools follows immediately form the above asymptotic stability theorem