schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

on a rational approximation problem in the real hardy space h 2 1 introduction the problem of finding a rational approximation to a holomorphic function in a domain 52 often arises in practice let us give an example from system theory which has first motivated our work l system theory is concerned with the study of physical systems that can be described by a relation between inputs and outputs when considering discrete time systems it is a convention to denote by u z cksko ukzmk uker

improved stable approximants using the routh array a simple method for obtaining a stable reduced order k th order approximant g k s for a stable hlgh order n th order transfer function g s is described the method is an improvement over some previous methods 1 2 in that it not only ensures matching of the first k time moments of g s and g k s but it also ensures that the k 1 th time moment of g k s be as close as possible to the corresponding value in g s

routh pade approximation for interval systems presents a method for the reduction of the order of interval system the denominator of the reduced model is obtained by a direct truncation of the routh table of the interval system the numerator is obtained by matching the coefficients of power series expansions of the interval system and its reduced model a numerical example illustrates the proposed procedure

complex classical fields a framework for reflection positivity we explore a framework for complex classical fields appropriate for describing quantum field theories our fields are linear transformations on a hilbert space so they are more general than random variables for a probability measure our method generalizes osterwalder and schrader s construction of euclidean fields we allow complex valued classical fields in the case of quantum field theories that describe neutral particles

euclidean random fields obtained by convolution from generalized white noise we study euclidean random fields x over rd of the form x g f where f is a generalized white noise over rd and g is an integral kernel we give conditions for the existence of the characteristic functional and moment functions and we construct a convergent lattice approximation of x finally we perform the analytic continuation of the moment functions and the characteristic functional of x obtaining the corresponding relativistic functions on minkowski space

orthogonal rational functions with real coefficients and semiseparable matrices when one wants to use orthogonal rational functions orfs in system identification or control theory it is important to be able to avoid complex calculations in this paper we study orfs whose numerator and denominator polynomial have real coefficients these orfs with real coefficients rorfs appear when the poles and the interpolation points appear in complex conjugate pairs which is a natural condition further we deduce that there is a strong connection between rorfs and semiseparable matrices

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

multiple positive solutions for p laplacian m point boundary value problems on time scales let t be a time scale such that 0 email protected t a i 0 for i 1 m 2 let x i satisfy 0 x 1 x 2 x m 2 r t and i 1 m 2a i 1 we consider the following p laplacian m point boundary value problem on time scales f p u d t a t f t u t 0 email protected 0 t u 0 0 f p u d t email protected i 1m 2a email protected p u d x i where email protected c l d 0 t 0 and email protected c l d 0 t x 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and leggett williams fixed point theorems respectively in particular our criteria extend and improve some known results

spl gamma spl delta routh approximation for interval systems the paper presents the spl gamma spl delta routh approximation for interval systems the interval spl gamma s and spl delta s are evaluated for the higher order interval systems and then an rth order approximant is obtained by retaining the first r interval spl delta s and spl gamma s a numerical example illustrates the procedure

linear system reduction by impulse energy approximation a method is given for linear system reduction which is a more general form of the routh method the reduced models retain stability and a fuller contribution is made to the impulse response energy of the reduced system by appropriate selection of retained alpha and beta parameters it requires no more computation than the routh method and can be presented in a compact tabular form examples are given to illustrate the method

positive solutions of nonlinear second order m point boundary value problem abstract in this paper by using krasnoselskii s fixed point theorem of cone expansion compression type and under suitable conditions we present the existence of single and multiple positive solutions to the nonlinear second order m point boundary value problem u t a t f u t 0 0 t 1 u 0 0 u 1 i 1 m 2 a i u i where is a positive parameter a i 0 for i 1 2 m 3 and a m 2 0 i satisfy 0 1 2 m 2 1 and i 1 m 2 a i i 1 we derive an explicit interval of such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed and the existence of at least two solutions for in an appropriate interval is also discussed

multiple positive solutions for nth order m point boundary value problems with all derivatives abstract we investigate the existence of positive solutions for the boundary value problem u n t f t u t u t u n 2 t u n 1 t 0 0 t 1 u 0 u 0 u n 2 0 0 u n 1 1 i 1 m 2 k i u n 1 i where f 0 1 r n r is continuous k i 0 i 1 2 m 2 0 i 1 m 2 k i 1 we give at first the associated green s function and some of its properties then imposing growth conditions on f we obtain the existence of at least three positive solutions for the boundary value problem by using the five functional fixed point theorem finally we give an example to demonstrate our result

on linear system reduction by impulse energy approximation linear system reduction by impulse response energy approximation is analyzed and limitations are discussed to show that in general the claims made for the procedure are not true a numerical example is included

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

model order reduction of random parameter dependent linear systems this paper proposes a new method to perform model reduction of linear time invariant lti systems where parameters are random variables governed by probabilistic laws it combines the well known truncation balanced realization tbr technique together with the generalized polynomial chaos gpc formalism a powerful tool for uncertainty propagation gpc formalism is used to represent and compute a random parameter dependent balancing transformation rpd bt which puts the random lti system in a balanced form almost surely within the probabilistic range of the uncertain parameters model reduction is then performed by truncating almost surely weakly controllable and observable states yielding a random parameter dependent truncated balanced realization rpd tbr the truncation error s moments are shown to be bounded by hankel singular values moments which are also estimated using gpc formalism as an illustrative example the proposed method is applied to a simple mechanical model of a two degrees of freedom mass spring system with uncertain stiffness and damping

higher order m point boundary value problems on time scales in this paper we investigate the existence of positive solutions for nonlinear even order m point boundary value problems on time scales by means of fixed point theorems

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

positive solutions to singular multi point dynamic eigenvalue problems with mixed derivatives abstract this paper considers a singular m point dynamic eigenvalue problem on time scales t p t u t f t u t t 0 1 t u 0 i 1 m 2 a i u i u 1 p 1 u 1 i 1 m 2 b i p i u i we allow f t w to be singular at w 0 and t 0 by constructing the green s function and studying its positivity eigenvalue intervals in which there exist positive solutions of the above problem are obtained by making use of the fixed point index theory

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

algorithms for model reduction of large dynamical systems three algorithms for the model reduction of large scale continuous time time invariant linear dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described they rely on low rank approximations to the controllability and observability gramians which can efficiently be computed by adi based iterative low rank methods the first two model reduction methods are closely related to the well known square root method and schur method which are balanced truncation techniques the third method is a heuristic balancing free technique the performance of the model reduction algorithms is studied in numerical experiments

equivalence of euclidean and wightman field theories a new inversion formula for the laplace transformation of tempered distributions with supports in the closed positive semiaxis is obtained the inverse laplace transform of a tempered distribution is defined by means of a limit of a special distribution constructed from this distribution the weak spectral condition on the euclidean green s functions implies that some of the limits needed for the inversion formula exist for any euclidean green s function with an even number of variables we then prove that the initial osterwalder schrader axioms 1 and the weak spectral condition are equivalent with the wightman axioms

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on time scales in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value pr

comments on the computation of interval routh approximants in bandyopadhyay et al 1994 1997 the routh approximation method was extended to derive reduced order interval models for linear interval systems in this paper the authors show that 1 interval routh approximants to a high order interval transfer function depend on the implementation of interval routh expansion and inversion algorithms 2 interval routh expansion algorithms cannot guarantee the success in generating a full interval routh array 3 some interval routh approximants may not be robustly stable even if the original interval system is robustly stable and 4 an interval routh approximant is in general not useful for robust controller design because its dynamic uncertainties in terms of robust frequency responses do not cover those of the original interval system

h sub spl infin model reduction with application to flexible systems in this note h sub spl infin model reduction of continuous time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method leading to the conclusion that the proposed method performs significantly better finally the proposed method is applied to the determination of a reduced order model of a flexible bar

a note on the model reduction problem a mixed method of model reduction is proposed it is based on the differentiation method suggested by gutman et al 1 and on the usual pade method more precisely the differentiation procedure is used to obtain the reduced order denominator thus ensuring stability preservation while the numerator is obtained by matching the first maclaurin expansion coefficients of the original system and model transfer functions the method is computationally very simple and may lead to satisfactory results as shown by an example where the original system transfer function is taken from the relevant literature

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

model reduction of discrete time systems through linear matrix inequalities in this paper model reduction of discrete time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method the results lead to the conclusion that the proposed method performs equivalently when the h 2 norm of the reduction error is considered and significantly better when the h norm is considered instead

an algorithmic method for the simplification of linear dynamic scalar systems a comprehensive method is proposed for obtaining reduced order models of a scalar linear time invariant system described by the transfer function g s the method is a viable alternative to the pade approximation technique for model order reduction it approximates the differential operations d i g s dsi proportional to the time moments by the divided difference equivalents and finally leads to linear equations in the unknown coefficients of the reduced model r s it is shown that a parameter governs the stability and the low frequency matching quality of the model heuristic criteria are given for selecting a proper the method is illustrated by some examples from the literature

on routh pade model reduction of interval systems this paper discusses another generalization of the direct routh table truncation method for interval systems it is shown that the existing generalization of the direct routh table truncation fails to produce a stable system in contradiction to the equivalent result for fixed coefficients systems the present method guarantees a stable reduced order model for interval systems as well

existence of multiple positive solutions for m point boundary value problems in banach spaces this paper deals with the positive solutions of m point nonlinear boundary value problem in banach spaces by using the fixed point theorem of strict set contractions some sufficient conditions for the existence of at least one or two positive solutions to m point boundary value problem in banach spaces are obtained an example illustrating the main results is given

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

positive solutions of m point boundary value problems for higher order ordinary differential equations abstract in this paper we study m point boundary value problems for higher order ordinary differential equation y 2 n t f t y t y t y 2 n 1 t 0 t 1 y 2 i 0 0 y 2 i 1 j 1 m 2 k i j y 2 i j 0 i n 1 where f is allowed to change sign and 0 0 1 2 m 2 m 1 1 we show sufficient conditions for the existence of at least two positive solutions by applying a new fixed point theorem in cones and the associated green s function in particular the second positive solutions for the above problem is not concave

dynamic siso and miso system approximations based on optimal laguerre models a general procedure based on the knowledge of the input and the output signals is proposed to approximate the prescribed linear time invariant lti systems by means of optimal laguerre models the main contribution of this paper is to apply the newton raphson s iterative technique to compute the so called optimal laguerre pole in a continuous time case or optimal time scale factor in a discrete time case and especially to show that the gradient and the hessian can be expressed analytically moreover the excitations used are not limited to the ones that ensure the orthogonality of the outputs of laguerre filters i e dirac delta or white noise as is usually done in existing methods however persistently exciting input signal s are used the proposed procedure will be directly formulated for siso systems siso systems being a special case with the number of inputs equal to one the proposed algorithm has direct applications in system identification model reduction and noisy modeling

stochastically positive structures on weyl algebras the case of quasi free states we consider quasi free stochastically positive ground and thermal states on weyl algebras in the imaginary time formulation in particular we obtain a new derivation of a general form of thermal quasi free state and give conditions when such a state is stochastically positive i e when it defines a periodic stochastic process with respect to imaginary time a so called thermal process then we show that the thermal process completely determines modular structure canonically associated with the quasi free thermal state on weyl algebra we discuss a variety of examples connected with free quantum field theories on globally hyperbolic stationary space times and models of quantum statistical mechanics

an improvement in the routh pade approximation techniques a method for approximating high order stable systems via lower order stable models is presented it is an improvement over previous routh pade methods since the denominator polynomial of the model transfer function even if based on the elements of a routh array contains two free parameters a systematic procedure is illustrated for evaluating besides the numerator coefficients such denominator parameters in order to ensure a good fit in the pade sense and a suitable stability margin

multi point boundary value problems on time scales at resonance abstract we study the nonlinear second order differential equation on a time scale u t f t u t u t e t t 0 1 t subject to the multi point boundary conditions u 0 0 u 1 i 1 m i u i and u 0 0 u 1 i 1 m i u i where t is a time scale such that 0 1 t i 0 1 t i 1 m and f is a continuous function satisfying a caratheodory type growth condition and e is a lebesgue integrable function our existence results are obtained by applying a coincidence degree theorem due to mawhin

three positive solutions for a nonlinear nth order m point boundary value problem abstract in this paper we consider the existence of at least three positive solutions for the nonlinear n th order m point boundary value problem u n t f t u 0 t 0 1 u 0 0 u 0 u n 2 0 0 u 1 i 1 m 2 k i u i where n 2 k i 0 i 1 2 m 2 0 1 2 m 2 1 the associated green s function for the n th order m point boundary value problem is first given and growth conditions are imposed on the nonlinearity f which yield the existence of multiple positive solutions by using the leggett williams fixed point theorem

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

existence results for an even order boundary value problem on time scales abstract let t be a time scale with t 1 t 2 t 3 t we investigate the existence of solutions to the nonlinear even order three point boundary value problem 1 n y 2 n t f t y t t t 1 t 3 t y 2 i 1 t 1 0 y 2 i t 3 y 2 i 1 t 3 y 2 i 1 t 2 0 i n 1 where n n t 2 t 1 t 3 0 and 1 are given constants

constructive field theory and applications perspectives and open problems in this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory they could give work for future mathematical physicists trained with constructive methods well into the 21st century

a generalization of kharitonov s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations kharitonov s four polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions to this end a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis the present work is motivated by two fundamental limitations of kharitonov s theorem namely 1 the theorem only applies to polynomials with independent coefficient perturbations and 2 it only applies to zeros in the left hand plane

several existence theorems of nonlinear m point boundary value problem for p laplacian dynamic equations on time scales abstract in this paper several existence theorems of positive solutions are established for nonlinear m point boundary value problem for p laplacian dynamic equations on time scales as an application an example to demonstrate our results is given the conditions we used in the paper are different from those in h r sun w t li positive solutions for nonlinear three point boundary value problems on time scales j math anal appl 299 2004 508 524 h r sun w t li positive solutions for nonlinear m point boundary value problems on time scales acta math sinica 49 2006 369 380 in chinese y wang c hou existence of multiple positive solutions for one dimensional p laplacian j math anal appl 315 2006 144 153 y wang w ge positive solutions for multipoint boundary value problems with one dimensional p laplacian nonlinear appl 66 6 2007 1246 1256

an iterative svd krylov based method for model reduction of large scale dynamical systems abstract in this paper we propose a model reduction algorithm for approximation of large scale linear time invariant dynamical systems the method is a two sided projection combining features of the singular value decomposition svd based and the krylov based model reduction techniques while the svd side of the projection depends on the observability gramian the krylov side is obtained via iterative rational krylov steps the reduced model is asymptotically stable matches certain moments and solves a restricted h 2 minimization problem we present modifications to the proposed approach for employing low rank gramians in the reduction step and also for reducing discrete time systems several numerical examples from various disciplines verify the effectiveness of the proposed approach it performs significantly better than the q cover a yousouff r e skelton covariance equivalent realizations with applications to model reduction of large scale systems in c t leondes ed control and dynamic systems vol 22 academic press 1985 pp 273 348 a yousouff d a wagie r e skelton linear system approximation via covariance equivalent realizations journal of math anal and appl 196 1985 91 115 and the least squares s gugercin a c antoulas model reduction of large scale systems by least squares linear algebra appl 415 2 3 2006 290 321 methods that have a similar projection structure to the proposed method also in terms of both the h 2 and h error measures its performance is comparable to or sometimes better than that of balanced truncation moreover the method proves to be robust with respect to the perturbations due to usage of approximate gramians

optimality conditions for truncated kautz networks with two periodically repeating complex conjugate poles presents optimality conditions for the approximation of a siso system by a truncated kautz network with two repeating complex conjugate poles both the continuous and the discrete time cases are discussed the author approaches the problem in a system approximation framework and he does not assume that the input signal is white or an impulse the results obtained generalize the results already known for truncated laguerre networks

existence of two solutions of m point boundary value problem for second order dynamic equations on time scales in this paper by means of a new twin fixed point theorem in a cone the existence of at least two positive solutions of m point boundary value problem for second order dynamic equations on time scales is considered

an improvement on routh approximation technique a modification of the routh approximant is introduced which results in a considerable improvement over the conventional routh approximation technique since some amount of arbitrariness is available in the time moment expressions of the conventional routh approximant it can be utilized to minimize the step response error while preserving the stability and moment matching property of the conventional routh approximant a numerical example illustrates the procedure

improved routh pade spl acute approximants a computer aided approach a geometric programming based computer aided method to derive a reduced order rth order approximant for a given stable siso linear continuous time system is presented in this method stability and the first r time moments markov parameters are preserved as well as the errors between a set of subsequent time moments markov parameters of the system and those of the model are minimized

comments on on routh pade model reduction of interval systems a numerical example is given to show that the model reduction method of interval systems proposed by dolgin and zeheb in the above paper cannot guarantee the stability of the reduced order interval models

robust stability under structured and unstructured perturbations the problem of robust stability for linear time invariant single output control systems subject to both structured parametric and unstructured h sub infinity perturbations is studied a generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time invariant dynamic system under perturbations of mixed type is presented the solution involves calculating the h sub infinity norm of a finite number of extremal plants the problem of calculating the exact structured and unstructured stability margins is then constructively solved a feedback control system containing a linear time invariant plant which is subject to both structured and unstructured perturbations is considered the case where the system to be controlled is interval is treated and a nonconservative easily verifiable necessary and sufficient condition for robust stability is given the solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered

geometric programming for optimal positive linear systems this article studies the parameter tuning problem of positive linear systems for optimizing their stability properties we specifically show that under certain regularity assumptions on the parameterization the problem of finding the minimum cost parameters that achieve a given requirement on a system norm reduces to a geometric program which in turn can be exactly and efficiently solved by convex optimization the flexibility of geometric programming allows the state input and output matrices of the system to simultaneously depend on the parameters to be tuned the class of system norms under consideration includes the h 2 norm h infty norm hankel norm and schatten p norm also the parameter tuning problem for ensuring the robust stability of the system under structural uncertainties is shown to be solved by geometric programming the proposed optimization framework is further extended to delayed positive linear systems where it is shown that the parameter tuning problem jointly constrained by the exponential decay rate the mathcal l 1 gain and the mathcal l infty gain can be solved by convex optimization the assumption on the system parameterization is stated in terms of posynomial functions which form a broad class of functions and thus allow us to deal with various interesting positive linear systems arising from for example dynamical buffer networks and epidemic spreading processes we present numerical examples to illustrate the effectiveness of the proposed optimization framework

on worst case approximation of feasible system sets via orthonormal basis functions this note deals with the approximation of sets of linear time invariant systems via orthonormal basis functions this problem is relevant to conditional set membership identification where a set of feasible systems is available from observed data and a reduced complexity model must be estimated the basis of the model class is made of impulse responses of linear filters the objective of the note is to select the basis function poles according to a worst case optimality criterion suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

stable partial pade approximations for reduced order trnsfer functions while the pade approximation can often be used to produce good reduced order transfer functions the method suffers from the disadvantage that a stable reduced order model is not always obtained for an original model that is stable a method is described for obtaining stable partial pade approximation reduced order models the method permits the determination of the effect of changes in the coefficients in the partial pade approximation on the poles of the reduced order transfer function by means of standard root locus plots

a fast adaptive model reduction method based on takenaka malmquist systems abstract an adaptive model reduction method is proposed for linear time invariant systems based on the continuous time rational orthogonal basis takenaka malmquist basis the method is to find an adaptive approximation in the energy sense by selecting optimal points for the rational orthogonal basis the stability of the reduced models holds and the steady state values of step responses are kept to be equal furthermore the method automatically ensures the reduced system to be in the hardy space h 2 the existence of the best approximation in the hardy space h 2 by n blaschke forms is proved in the proposed approach the effectivity of this method is illustrated through three well known examples

construction of relativistic quantum fields in the framework of white noise analysis we construct a class of euclidean invariant distributions h indexed by a function h holomorphic at zero these generalized functions can be considered as generalized densities w r t the white noise measure and their moments fulfill all osterwalder schrader axioms except for reflection positivity the case where f s h is 12s2 s r is a levy characteristic is considered in rev math phys 8 763 1996 under this assumption the moments of the euclidean invariant distributions h can be represented as moments of a generalized white noise measure ph here we enlarge this class by convolution with kernels g coming from euclidean invariant operators g the moments of the resulting euclidean invariant distributions hg also fulfill all osterwalder schrader axioms except for reflection positivity for no nontrivial case we succeeded in proving reflection positivity nevertheless an analytic extension to wightman functions can be performed these functions fulfill all wightman axioms except for the po

positive solutions for multi point boundary value problem on the half line this paper presents a variety of existence results for nonlinear multi point boundary value problem on the half line in particular we consider x t px t qx t f t x t 0 t 0 x 0 x 0 i 1nkix i a limt x t ert b r 0 p p2 4q2 existence results are established using fixed point theorems on cone

euclidean quantum vector fields we study quantum vector fields in euclidean space time these fields can be identified with generalized random vector fields which we study in terms of their covariance we prove that the conditions of translational invariance covariance with respect to some representation j of the orthogonal group o n where none of the irreducible components j is trivial and the condition of reflection positivity cannot be fulfilled at the same time unless the test function space is restricted by some gauge condition however if the representation is trivial i e if every matrix in o n is mapped to the identity we can explicitly write down covariance matrices which lead to gaussian fields which fulfill all conditions in the axiomatic framework

further discussion on impulse energy approximation recent criticisms by rao about impulse energy approximation are answered in detail further ideas are put forward as to how weighted energy parameters may be used to determine the reduced models for step inputs

identification and rational l 2 approximation a gradient algorithm this paper deals with the identification of linear constant dynamical systems when formalized as a rational approximation problem the criterion is the l2 norm of the transfer function which is of interest in a stochastic context the problem can be expressed as nonlinear optimization in a hilbert space but standard algorithms are usually not well adapted we present a generic recursive procedure to find a local optimum of the criterion in the case of scalar systems our methods are borrowed from differential theory mixed with a bit of classical complex analysis to our knowledge the algorithm described in this paper is the first that ensures convergence to a local minimum

author s reply to comments on on routh pade model reduction of interval systems the paper is reply to the article by shih feng yang see ibid p 273 4 2005 previously dolgin and zeheb 2003 it was shown that the existing generalization of the direct routh table truncation method for interval systems fails to produce a stable system additionally it was shown how to extend the method to ensure the stability of the resulting interval system although the main statement of dolgin and zeheb 2003 is correct there is however an omission in the proposed algorithm of building interval routh table the newly calculated line in the table may be inconsistent with the last existing line two additional conditions should be formulated to avoid this situation the main idea is to shrink the uncertainty of the elements of the last existing line of the table in the procedure of building the new line

model reduction of uncertain systems retaining the uncertainty structure model reduction of high order linear in parameters discrete time systems is considered the main novelty of the paper is that the coefficients of the original system mod el are assumedto be known only within given intervals andthe coefficients of the derived reduced order model are also obtained in intervals such that the complex value sets of the uncertain original andred ucedmod els will be optimally close to each other on the unit circle the issue of inclusion of one value set in another is also addressed in the paper the meaning of model reduction is defined for linear in parameters systems the algorithm for obtaining the value sets of such systems is derived in the paper then applying a novel approach the infinity norm of distance between two polygons representing the original and the reduced uncertain systems is minimized a noteworthy point is that by a special definition of this distance the problem is formulated as a linear semi infinite programming problem with linear constraints thus reducing significantly the computational complexity numerical example is provided 2004 elsevier b v all rights reserved

scaled impulse energy approximation for model reduction it is shown that the impulse energy approximation technique for model reduction can be improved by scaling in the frequency domain the method remains simple to use and retains the stability property of impulse energy approximation criteria are given for choosing an appropriate scaling parameter an example illustrates the technique