computation and analysis of the asymptotic expansions of the compound means we derive algorithms for computing asymptotic expansion of the composite mean of two arbitrary means m and n then we analyse asymptotic behaviour of the compound mean mn examples and application to some classical means are also presented

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

combined instrumental variable and subspace fitting approach to parameter estimation of noisy input output systems the paper considers the problem of estimating the parameters of linear discrete time systems from noise corrupted input output measurements under fairly general conditions the output and input noises may be auto correlated and they may be cross correlated as well by using the instrumental variable iv principle a covariance matrix is obtained the singular vectors of which bear complete information on the parameters of the system under study a weighted subspace fitting wsf procedure is then employed on the sample singular vectors to derive estimates of the parameters of the system the combined iv wsf method proposed in the present paper is noniterative and simple to use its large sample statistical performance is analyzed in detail and the theoretical results so obtained are used to predict the behavior of the method in samples with practical lengths several numerical examples are included to show the agreement between the theoretically predicted and the empirically observed performances

symmetric family of fredholm operators of indices zero stability of essential spectra and application to transport operators abstract in this paper we prove that if the product a a 1 a n is a fredholm operator where the ascent and descent of a are finite then a j is a fredholm operator of index zero for all j 1 j n where a 1 a n be a symmetric family of bounded operators next we investigate a useful stability result for the rakocevic schmoeger essential spectra moreover we show that some components of the fredholm domains of bounded linear operators on a banach space remain invariant under additive perturbations belonging to broad classes of operators a such as a m 1 where is a measure of noncompactness we also discuss the impact of these results on the behavior of the rakocevic schmoeger essential spectra further we apply these latter results to investigate the rakocevic schmoeger essential spectra for singular neutron transport equations in bounded geometries

using transfer function parameter changes for damage detection of structures a novel approach is presented for damage detection of large flexible structures by using the parameter change of the transfer function first an interval modeling technique which represents the system uncertainty under the environmental change via the intervals of transfer function parameters is used to distinguish the structural damage from the environmental change in this paper a coherence approach is developed for locating the damage position when the structural damage is observed only a few sensors are required in using the proposed coherence approach for damage detection this has the advantage of using the proposed algorithm for practical applications also this approach has the flexibility of using the multi input and multi output system a nine bay truss example is used to demonstrate and verify the approach developed nomenclature a b denominator and numerator parameters of transfer function c coherence of the tested system to damage g interval model g transfer function k number of modes m number of outputs n number of tests for environmental change p parameter vector of transfer function r magnitude ratio of the tested system to damage r jr magnitude ratio bounds w weight of parameter change wa w weights of intervals for interval model x y unit vectors of cartesian coordinate system ap parameter change vector superscripts

a characterization of some subsets of schechter s essential spectrum and application to singular transport equation the purpose of this paper is to provide a detailed treatment of some subsets of schechter s essential spectrum of closed densely defined linear operators subjected to additive perturbations our results are used to describe the essential approximate point spectrum and the essential defect spectrum of singular neutron transport operators in bounded geometries

identifying mimo hammerstein systems in the context of subspace model identification methods in this paper we outline the extension of the moesp family of subspace model identification schemes to the hammerstein type of nonlinear system two types of identification problem are considered the first type assumes the polynomial structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para metrization of the static nonlinearity the second type addresses the identification of both the linear dynamic part and the static nonlinearity where only limited a priori information regarding the structure of the nonlinearity is available the improved robustness properties of the algorithms developed for this second type of hammerstein identification problem over existing correlation based schemes is illustrated by a numerical example

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

subspace algorithms for the identification of multivarible dynamic errors in variables models abstract we consider the problem of identifying multivariable finite dimensional linear time invariant systems from noisy input output measurements apart from the fact that both the measured input and output are corrupted by additive white noise the output may also be contaminated by a term which is caused by a white input process noise furthermore all these noise processes are allowed to be correlated with each other we shall develop a solution to this problem in the framework of subspace identification and we shall show that our algorithms give consistent estimates when the system is operating in open or closed loop two realistic simulation studies are presented to demonstrate the practical applicability of the proposed algorithms 1997 elsevier science ltd

a characterization of the schechter essential spectrum on banach spaces and applications abstract in a recent article by the author c r acad sci paris ser i 331 2000 525 530 boll un mat ital 2002 to appear the schechter spectrum of closed densely defined linear operators has been characterized on spaces which possess the dunford pettis property or which are isomorphic to one of the spaces l p p 1 the purpose of the present work is to extend this analysis to the case of banach spaces further we apply the obtained results to investigate the schechter essential spectrum of one dimensional transport equations with different boundary conditions

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

fredholm semi fredholm perturbations and essential spectra abstract this paper is devoted to the investigation of the stability of the various essential spectra of closed densely defined linear operators under perturbations belonging to any two sided ideal of the algebra of bounded linear operators contained in the set of fredholm perturbations our results generalize many known ones in the literature and in particular extend and unify those obtained by k latrach 1999 j math anal appl 233 607 623 and k latrach and a jeribi 1998 j math anal appl 225 461 485 they are used to describe the essential spectra of one dimensional transport equations with anisotropic scattering and abstract boundary conditions

essential spectra on spaces with the dunford pettis property the purpose of this paper is to investigate the invariance under weakly compact perturbations of various essential spectrums of closed densely defined linear operators acting on banach spaces which possess the dunford pettis property both bounded and unbounded perturbations are considered

bernoulli polynomials and asymptotic expansions of the quotient of gamma functions the main subject of this paper is the analysis of asymptotic expansions of wallis quotient function c x t c x s and wallis power function c x t c x s 1 t s when x tends to infinity coefficients of these expansions are polynomials derived from bernoulli polynomials the key to our approach is the introduction of two intrinsic variables a 12 t s 1 and b 14 1 t s 1 t s which are naturally connected with bernoulli polynomials and wallis functions asymptotic expansion of wallis functions in terms of variables t and s and also a and b is given application of the new method leads to the improvement of many known approximation formulas of the stirling s type

asymptotic analysis of the iterative power means abstract we investigate the asymptotic expansion of the compound mean obtained by the iterative process of two power means we present the stationary and convergence properties of the coefficients in the expansions

on a characterization of the essential spectra of some matrix operators and application to two group transport operators in this paper we investigate the essential approximate point spectrum and the essential defect spectrum of a 2 2 block operator matrix on a banach space furthermore we apply the obtained results to two group transport operators in the banach space l p a a 1 1 l p a a 1 1 a 0 p 1

system identification and model reduction for a single link flexible manipulator a new model reduction and updating technique is proposed and applied in modelling of a single link flexible manipulator the observability range space extraction algorithm is used to generate an initial overparameterized state space model the identified model is transformed into modal realization the modal responses of individual modes are evaluated a new measure is proposed to quantify the contribution of individual modes to the total responses using the proposed measure a reduced order model is obtained by retaining the most significant modes to improve model accuracy either the reduced input or output matrix can be recalculated by a proposed method several critical issues related to the experimental identification are addressed experimental identification results are presented to illustrate the proposed technique

qsvd approach to on and off line state space identification moonen et al 1989 a presented an svd based identification scheme for computing state space models for multivariable linear time invariant systems in the present paper this identification procedure is reformulated making use of the quotient singular value decomposition qsvd here the input output error co variance matrix can be taken into account explicitly thus extending the applicability of the identification scheme to the case were the input and output data are corrupted by coloured noise it turns out that in practice due to the use of various pre filtering techniques anti aliasing etc this latter case is most often encountered the extended identification scheme explicitly compensates for the filter characteristics and the consistency of the identification results follows from the consistency results for the qsvd the usefulness of this generalization is demonstrated the development is largely inspired by recent progress in total least squares solution techniques van huffel 1989 for

suppression of bursting abstract we investigate the possibility of using a single small amplitude control input and feedback to stabilize equilibrium sets in a class of highly nonlinear o 2 symmetric dynamical systems possessing structurally stable heteroclinic cycles the leading order behavior near the equilibria is bilinear and homogeneous in the state variables while nonlinearities representing the symmetry breaking effect of the controller are crucial after a series of simplifying transformations we use ideas from optimal control theory to construct a stabilizing controller this study is motivated by the desire to stabilize the burst sweep cycle in low dimensional models of a turbulent boundary layer in the last two sections we apply the techniques to the 10 dimensional system of aubry et al 1988 kw bilinear systems dynamical systems heteroclinic cycles normal forms optimal control symmetry

subspace model identification part 1 the output error state space model identification class of algorithms in this paper we present two novel algorithms to realize a finite dimensional linear time invariant state space model from input output data the algorithms have a number of common features they are classified as one of the subspace model identification schemes in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input output data this structure is then exploited in the calculation of a realization another common feature is their algorithmic organization an rq factorization followed by a singular value decomposition and the solution of an overdetermined set or sets of equations the schemes assume that the underlying system has an output error structure and that a measurable input sequence is available the latter characteristic indicates that both schemes are versions of the mimo output error state space model identification moesp approach the first algorithm is denoted in particular as the elementary moesp scheme

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

asymptotic expansions of integral means and applications to the ratio of gamma functions integral means are important class of bivariate means in this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean it is based on explicit solving the equation of the form b a x c x where asymptotic expansions of b and c are known the results are illustrated by calculation of some important integral means connected with gamma function

comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models the estimation of the parameters of a transfer function model is considered relationships between the total least squares tls and instrumental variable iv approaches are outlined both methods

comparison of several system identification methods for flexible structures abstract in the past few years various methods of identifying structural dynamics models from modal testing data have appeared this paper presents a comparison of four of these algorithms the eigensystem realization algorithm era the modified version era dc where dc indicates that it makes use of data correlations the q markov cover algorithm and an algorithm due to moonen demoor vandenberghe and vandewalle mdvv the comparison is made using a five mode computer model of the 20 m mini mast truss structure at the nasa langley research center and various noise levels are superimposed to produce simulated data the results show that for the example considered era dc generally gives the best results that era dc is always at least as good as era which is shown to be a special case of era dc that q markov requires the use of significantly more data than era dc to produce comparable results and that in some situations q markov cannot produce comparable results the mdvv algorithm can avoid pre processing of data to obtain markov parameters but requires significantly larger matrix singular value decomposition for large data sets