linear and nonlinear algorithms for identification in h sub infinity with error bounds a linear algorithm and a nonlinear algorithm for the problem of system identification in h sub infinity posed by helmicki et al 1990 for discrete time systems are presented the authors derive some error bounds for the linear algorithm which indicate that it is not robustly convergent however the worst case identification error is shown to grow as log n where n is the model order a robustly convergent nonlinear algorithm is derived and bounds on the worst case identification error in the h sub infinity norm are obtained

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

a weak star convergence result for orthogonal rational functions we prove a weak star convergence result for orthogonal rational functions on the interval 1 1 which generalizes a well known result by rakhmanov math ussr sb 32 1977 199 as an application we use this result to approximate a certain integral which occurs in the computation of orthogonal rational functions

algorithm of adaptive fourier decomposition the present paper is a continuing work on the recently established adaptive fourier decomposition afd mainly stressing on the algorithm aspect including algorithm analysis and numerical examples afd is a variation and realization of greedy algorithm matching pursuit suitable for the hardy h2 and the l2 spaces applying afd to a given signal one obtains a series expansion in the basic signals called mono components that possess non negative analytic phase derivatives functions or equivalently meaningful analytic instantaneous frequencies afd is shown to be robust with computational complexity comparable with dft consistent to the greedy algorithm principle experiments show that afd produces pre mono component series with efficient energy decay that also leads to efficient pointwise convergence both in terms of computer running time

on the time complexity of worst case system identification in this paper we treat a general worst case system identification problem this problem is worst case with respect to both noise and system modeling uncertainty we consider this problem under various a priori information structures we determine bounds on the minimum duration identification experiment that must be run to identify the plant to within a specified guaranteed worst case error bound our results are algorithm independent we show that this minimum duration is prohibitively long based on our results we suggest that worst case with respect to noise system identification requires unrealistic amounts of experimental data

on two functions of a matrix with positive definite hermitian part let a be a square complex matrix with positive definite hermitian part h a a a h 2 and let f a g a be two functions defined by f a h a 1 1 g a a 1 a h this paper derives

on eigenvalue variations of rayleigh quotient matrix pencils of a definite pencil abstract let a b be a definite matrix pencil of order n i e both a and b are n n hermitian and c a b def min xe c n x 2 1 x h a ib x 0 suppose y is an n l matrix with full column rank whose column vectors span an approximate invariant subspace for a b this note investigates the relation between eigenvalues of a b and those of y h ay y h by our result for the spectral norm improves sun s linear algebra appl 139 253 267 1990 we also present bounds in frobenius norms and in general unitarily invariant norms

robust identification in h abstract we consider system identification in the banach space h in the framework proposed by helmicki jacobson and nett it is shown that there is no robustly convergent linear algorithm for identifying exponentially stable systems in the presence of noise which is not tuned to prior information about the unknown system or noise various nonlinear algorithms some closely related to one of gu and khargonekar are analysed and results on trigonometric interpolation used to provide new error bounds an application of these techniques to approximation is given and finally some numerical results are provided for illustration

computing orthogonal rational functions with poles near the boundary computing orthogonal rational functions is a far from trivial problem especially for poles close to the boundary of the support of the orthogonality measure in this paper we analyze some of the difficulties involved and present two different approaches for solving this problem

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

worst case analysis of the least squares method and related identification methods abstract we consider worst case analysis of system identification under less restrictive assumptions on the noise than the l bounded error condition it is shown that the least squares method has a robust convergence property in l 2 identification but lacks a corresponding property in l 1 identification as well as in all other non hilbert space settings the latter result is in stark contrast with typical results in asymptotic stochastic analysis of the least squares method furthermore it is shown that the khintchine inequality is useful in the analysis of least l p identification methods

orthogonal rational functions for system identification numerical aspects recently there has been a growing interest in the use of orthogonal rational functions orfs in system identification there are many advantages over more classical techniques probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 the so called malmquist basis the attention has been on the development of methods using this basis however for some discrete identification problems this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved in this note we give an algorithm based on a more general system of orf to overcome the numerical problem and which allows for a fast order update of the estimate

a limited feedback joint precoding for amplify and forward relaying this paper deals with the practical precoding design for a dual hop downlink with multiple input multiple output mimo amplify and forward relaying first assuming that full channel state information csi of the two hop channels is available a suboptimal dual hop joint precoding scheme i e precoding at both the base station and relay station is investigated based on its structure a scheme of limited feedback joint precoding using joint codebooks is then proposed which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased finally the joint codebook design for the limited feedback joint precoding system is analyzed and results reveal that independent codebook designs at the base station and relay station using the conventional grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or ber performance close to the one using the optimal centralized codeword selection scheme while having lower computational complexity and shorter feedback delay

symmetric matrix pencils abstract a significant number of matrix eigenvalue problems quadratic or linear are best reformulated as pencils a m in which both a and m are real and symmetric some examples are given and then the canonical forms are re examined to explain the role of the sign characteristic attached to real eigenvalues in addition we examine the limitations on the use of the rayleigh quotient functional x ax x mx in describing the eigenvalues this sheds new light on the class of definite pencils and the stability of their eigenvalues under perturbations the reduction of indefinite pencils to useful sparse forms is mentioned

system identification with generalized orthonormal basis functions a least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function where the expansion is in terms of recently introduced generalized basis functions the basis functions are orthogonal in h2 and generalize the pulse laguerre and kautz bases one of their important properties is that when chosen properly they can substantially increase the speed of convergence of the series expansion this leads to accurate approximate models with only a few coefficients to be estimated explicit bounds are derived for the bias and variance errors that occur in parameter estimates as well as in the resulting transfer function estimates

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

sample complexity of worst case h identification abstract we show that the sample complexity of qorst case h identification is of order n 2 by proving that the minimal length of a fractional h cover for c n regarded as the linear space of complex valued sequences of length n is of order n 2 a unit vector u in l is a fractional h cover for c n if for some 0 h h for all rh c n where h z j 0 n 1 h j z j is the z transform of h we also give similar results for real valued sequences

robust identification and interpolation in h abstract we consider system identification in h in the framework proposed by helmicki jacobson and nett an algorithm using the jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems it is shown that this and similar identification algorithms can be successfully combined with a model reduction procedure to produce low order models connections with the nevanlinna pick interpolation problem are explored and an algorithm is given in which the identified model interpolates the given noisy data some numerical results are provided for illustration finally the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions

robust identification and galois sequences abstract worst case l1 identification is studied for bibo stable linear shift invariant systems it is shown that the chebyshev identification method when used with galois input designs satisfies a certain robust convergence property and provides l1 model error bounds in worst case identification of bibo stable systems with a uniformly bounded noise set up the robust identification methodology developed is compatible with the modelling requirements of modern robust control design

a frequency domain iterative identification algorithm using general orthonormal basis functions in this paper a two step frequency domain identification algorithm is proposed in which the identified model is parameterized in terms of general orthonormal basis functions furthermore an update scheme is presented where the poles of the basis functions are adjusted iteratively and the convergence properties of this scheme with respect to unknown but bounded noise are studied the algorithm is applied to experimental frequency response data obtained from a compact disk player

music like doa estimation without estimating the number of sources this paper presents a new direction of arrival doa estimation algorithm where doa estimation is realized in the framework of beamforming by introducing a new optimization problem the new optimization problem aims to minimize the variance of the array output subject to retaining the output power at the look direction and precluding a trivial solution the proposed algorithm is equivalent to the multiple signal classification music algorithm in some special cases it is therefore named as the music like method however different from the classical music algorithm the new method is not based on subspace decomposition and the number of sources is hence not required for direction finding this enables us to avoid performance deterioration caused by incorrect source number estimation the effectiveness and advantage of the proposed algorithm is theoretically investigated and computational complexity is also addressed to verify the theoretical analysis computer simulations are implemented and comparisons with other algorithms are made

a generalized orthonormal basis for linear dynamical systems in many areas of signal system and control theory orthogonal functions play an important role in issues of analysis and design in this paper it is shown that there exist orthogonal functions that in a natural way are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l sub 2sup n to this end use is made of balanced realizations of inner transfer functions the orthogonal functions can be considered as generalizations of for example the pulse functions laguerre functions and kautz functions and give rise to an alternative series expansion of rational transfer functions it is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion i e to obtain a good approximation by retaining only a finite number of expansion coefficients consequences for identification of expansion coefficients are analyzed and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

a note on stewart s theorem for definite matrix pairs abstract let a and b be n n hermitian matrices the matrix pair a b is called definite pair and the corresponding eigenvalue problem ax bx is definite if c a b inf x 1 h a ib x 0 in this note we develop a uniform upper bound for differences of corresponding eigenvalues of two definite pairs and so improve a result which is obtained by g w stewart 2 moreover we prove that this upper bound is a projective metric in the set of n n definite pairs

robust identification in the disc algebra using rational wavelets and orthonormal basis functions worst case identification using corrupted frequency response measurements is considered in a framework which allows one to consider a variety of rational basis functions these include laguerre models kautz models and rational wavelets conditions are given for model sets to be complete in the disc algebra and examples are given explicit error bounds are provided for approximate modelling using specific basis functions

a class of algorithms for identification in h abs traet in this paper a class of algorithms for the problem of system identification in are investigated these algorithms are characterized by a two stage structure and involve a class of window functions some conditions in terms of properties of the window functions are derived which guarantee robust convergence of the algorithms identification errors are analyzed for several common window functions this leads to some insights into the trade off between the error induced by approximation and that due to noise

a class of algorithms for identification in h sub infinity continuous time case the problem of system identification in h sub infinity for the continuous time case is investigated it is shown that the class of systems with a lower bound on the relative stability an upper bound on the steady state gain and an upper bound on the roll off rate is admissible this allows one to develop a class of robustly convergent nonlinear algorithms the algorithms in this class have a two stage structure and are characterized by the use of window functions explicit worst case error bounds in h sub infinity norm between the identified model and the unknown system are given for a particular algorithm an example is provided to illustrate the application of the results obtained

bifurcation at multiple eigenvalues and stability of bifurcating solutions if k is a bounded linear operator from the real banach space u into the real banach space v and u r v has the value zero at 0 0 the existence and linear stability of the equilibrium solutions of the dynamical system k dudt u which are close to the origin in u r are studied it is assumed that u 0 0 u v is a freholm operator of index zero the only restriction on the dimension of the null space of u 0 0 and the order of vanishing at 0 0 of restricted to the null space of d 0 0 u r v is that they both be finite positive integers the main result gives conditions under which the equation which determines the equilibrium solutions in a neighborhood of the origin also determines the stability of these equilibrium solutions

brief synthesis of complete rational orthonormal bases with prescribed asymptotic order in this paper a method to construct complete rational orthonormal model sets with prescribed asymptotic order is presented for continuous time systems two special cases that illustrate the application of the method are studied in the first case this method is shown to produce the generalized laguerre functions which form a complete model set for h 2 and have asymptotic order two in both cases this method is equivalent to calculating toeplitz determinants generated by a rational function the latter problem is reduced to finding solution of a linear finite difference equation

robust identification of strongly stabilizable systems for strongly stabilizable systems for which a strongly stabilizing controller is known approximately the authors consider system identification in the graph gap and chordal metrics using robust h sub infinity identification of the closed loop transfer function in the framework proposed by a j helmicki et al 1990 error bounds are derived showing that robust convergence is guaranteed and that the identification can be satisfactorily combined with a model reduction step two notions of robust identification of stable systems are compared and an alternative robust identification technique based on smoothing which can be used to yield polynomial models directly is developed

worst case system identification in h sub spl infin validation of a priori information essentially optimal algorithms and error bounds resolves several important open issues pertaining to a worst case control oriented system identification problem known as identification in h sub spl infin first a method is presented for developing confidence that certain a priori information available for identification is not invalid this method requires the solution of a certain nondifferentiable convex program second an essentially optimal identification algorithm is constructed this algorithm is worst case strongly optimal to within a factor of two finally new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm interestingly the development of each of these results draws heavily upon the classical nevanlinna pick interpolation theory as such the authors results establish a clear link between the areas of system identification and optimal interpolation theory both the formulation and techniques in this paper are applicable to problems where the frequency data available for identification may essentially be arbitrarily distributed

rational basis functions for robust identification from frequency and time domain measurements this paper investigates the use of general bases with fixed poles for the purposes of robust estimation these bases which generalise the common fir laguerre and two parameter kautz ones are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied it is also shown that by using a min max criterion these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified the key idea facilitating this analysis is to re parameterise the chosen model structures into a new one with equivalent fixed poles but for which the basis functions are orthonormal in h 2 d

subspace based multivariable system identification from frequency response data two noniterative subspace based algorithms which identify linear time invariant mimo multi input multioutput systems from frequency response data are presented the algorithms are related to the recent time domain subspace identification techniques the first algorithm uses equidistantly in frequency spaced data and is strongly consistent under weak noise assumptions the second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure

hard frequency domain model error bounds from least squares like identification techniques the problem of deriving so called hard error bounds for estimated transfer functions is addressed a hard bound is one that is sure to be satisfied i e the true system nyquist plot will be confined with certainty to a given region provided that the underlying assumptions are satisfied by blending a priori knowledge and information obtained from measured data it is shown how the uncertainty of transfer function estimates can be quantified the emphasis is on errors due to model mismatch the effects of unmodeled dynamics can be considered as bounded disturbances hence techniques from set membership identification can be applied to this problem the approach taken corresponds to weighted least squares estimation and provides hard frequency domain transfer function error bounds the main assumptions used in the current contribution are that the measurement errors are bounded that the true system is indeed linear with a certain degree of stability and that there is some knowledge about the shape of the true frequency response

laguerre series approximation of infinite dimensional systems laguerre fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems specifically time domain supremum and l1 norm convergence results and frequency domain h norm convergence results are given for laguerre fourier approximations it is also shown that the theory of laguerre polynomials solves explicitly the problem of determining laguerre fourier approximations for a large class of delay systems furthermore it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems

pencils of complex and real symmetric and skew matrices abstract this expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices the treatment is in the spirit of the well known book of gantmacher on matrix theory and may be regarded as a supplement to gantmacher s chapters on pencils of matrices

stability behavior for unsupervised learning abstract we consider models proposed by oja karhunen cox and adams for a task of unsupervised learning questions of existence of solutions and stability behavior of those solutions are addressed we also discuss the impact of temporary connections in the stability of the learning process

stability of solutions bifurcating from multiple eigenvalues let x and y be real banach spaces and g x r be a twice continuously differentiate function which is not necessarily linear suppose g u0 0 0 and the dimension of the null space of gu u0 0 is m where 1 m usually s u g u 0 in a neighborhood of u0 0 consists of a finite number of curves emanating from u0 0 we will determine the stability of points u in s i e the maximum of the real parts of the spectrum of gu u for each u s using a general perturbation theorem of kato our results contain as a special case the stability theorems of crandall and rabinowitz for the case m 1 we will also tie our stability theorems together with some bifurcation results of decker and keller finally we apply our results to systems of reaction diffusion equations

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

suboptimal algorithms for worst case identification in h sup spl infin and model validation new algorithms based on convex programming are proposed for worst case system identification the algorithms are optimal within a factor of two asymptotically further model validation or data consistency is embedded in the identification process explicit worst case identification error bounds in the h sup spl infin norm are also derived for both uniformly and nonuniformly spaced frequency response samples

set membership identification of systems with parametric and nonparametric uncertainty a method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented in the disturbance free case the parameter set estimate is guaranteed to contain the parameter set of the true plant in the presence of stochastic disturbances the parameter set estimate obtained from finite data records is shown to have the property that it contains the true plant parameter set with probability one as the data length tends to infinity

a perturbation bound for definite pencils we attempt to generalize a well known result on spectral variations of a hermitian matrix due to mirsky to the definite generalized eigenvalue problem we also point out that some results on perturbations of definite pencils due to stewart can be slightly improved

generalized fourier and toeplitz results for rational orthonormal bases this paper provides a generalization of certain classical fourier convergence and asymptotic toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one but rather a rational generalization which encompasses the trigonometric one as a special case these generalized fourier and toeplitz results have particular application in dynamic system estimation theory specifically the results allow a unified treatment of the accuracy of least squares system estimation using a range of model structures including those that allow the inclusion of prior knowledge of system dynamics via the specification of fixed pole or zero locations

discrete time system modelling in with orthonormal basis functions abstract in this paper model sets for linear time invariant systems spanned by fixed pole orthonormal bases are investigated the obtained model sets are shown to be complete in l p t 1 the lebesque spaces of functions on the unit circle t and in c t the space of periodic continuous functions on t the l p norm error bounds for estimating systems in l p t by the partial sums of the fourier series formed by the orthonormal functions are computed for the case 1 some inequalities on the mean growth of the fourier series are also derived these results have application in estimation and model reduction

hopf bifurcation at multiple eigenvalues with zero eigenvalue on donne des resultats locaux relies a la bifurcation de hopf pour des equations paraboliques la partie lineaire autour du point d equilibre peut avoir des valeurs propres nulles

controller design for plants with structured uncertainty this paper addresses the problem of designing feedback controllers to achieve good performance in the presence of structured plant uncertainty and bounded but unknown disturbances a general formulation for the performance robustness problem is presented and exact computable conditions are furnished these conditions are then utilized for synthesizing robust controllers which involves solving l1 optimization problems these solutions are computed using the duality theory of lagrange multipliers approximations and computational issues are discussed

generalized eigenvalues of a definite hermitian matrix pair abstract in this note we study some basic properties of generalized eigenvalues of a definite hermitian matrix pair in particular we prove an interlacing theorem and a minimax theorem we also obtain upper bounds for the variation of the generalized eigenvalues under perturbation these results extend and improve those of r c li j g sun and g w stewart on the topic

nontrivial harmonic waves with positive instantaneous frequency abstract the concept of time varying frequency is fundamental in communications and nature one description of a time varying frequency is the instantaneous frequency of a signal our concern is the design of analytic signals with nonlinear phase and positive instantaneous frequency in this paper a kind of nontrivial orthonormal harmonic waves are derived by applying the gram schmidt procedure to the blaschke products furthermore we show the orthonormal harmonic waves satisfy the analytic condition and have positive instantaneous frequencies which are tightly associated with the average frequencies of the two mono component analytic signals at each time as a consequence non stationary signals can be decomposed into the superposition of nontrivial harmonic waves related conclusions are established for the orthonormal analytic signals on the whole time range

relative eigenvalues of a definite matrix pair abstract let a and b be hermitian matrices and let c a b min x 2 1 xh a ib x the matrix pair a b is called a definite pair and the corresponding eigenvalue problem ax bx is definite if c a b 0 the relationship between the eigenvalues of a b and those of a definite pair of the form xh1ax1 xh1bx1 is studied in this paper the eigenvalues of xh1ax1 xh1bx1 are said to be the relative eigenvalues of a b with respect to the subspace r x1 from the main result of this paper one can deduce a corresponding conclusion on hermitian matrices

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

worst case identification in e 2 linear and nonlinear algorithms abstract we consider worst case identification in the l2 norm given an unknown system h l1 one wishes to choose bounded inputs u l such that given finitely many corrupted output measurements y k 0 k of y h u where is noise assumed small one can construct an approximation g with g h 2 0 as 0 and n it is shown that inputs can be chosen such that to identify a sequence of length n with an l2 error of o one requires only o n measurements a numerical example is inclu

estimation of the eigenvalues of ab for a 0 b 0 abstract for positive definite hermitian matrices a and b we obtain an upper and a lower bound for the eigenvalues of ab in terms of those of a and b

on the principle of reduced stability abstract the principle of reduced stability says that the stability of bifurcating stationary or periodic solutions is given by the finite dimensional bifurcation equation obtained by the method of lyapunov schmidt to be more precise the linearized stability is governed by the linearization of the bifurcation equation about the bifurcating branch of solutions and in particular by the signs of the real parts of the perturbation of the eigenvalues along this branch this principle is true for simple eigenvalue bifurcation whereas it may be false for higher dimensional bifurcation equations a condition for the validity of that principle is given a counterexample shows that it cannot be dropped in general

system identification by discrete rational atoms a novel adaptive frequency domain system identification method for linear time invariant systems is proposed in this paper it finds poles for discrete rational atoms with discrete frequency responses the theoretical foundation including adaptive decomposition principle and decomposition convergence rate is established the algorithm of the adaptive pursuit is also provided in this paper

on perturbations of matrix pencils with real spectra perturbation bounds for the generalized eigenvalue problem of a diagonalizable matrix pencil a ab with real spectrum are developed it is shown how the chordal distances between the generalized eigenvalues and the angular distances between the generalized eigenspaces can be bounded in terms of the angular distances between the matrices the applications of these bounds to the spectral variations of definite pencils are conducted in such a way that extra attention is paid to their peculiarities so as to derive more sophisticated perturbation bounds our results for generalized eigenvalues are counterparts of some celebrated theorems for the spectral variations of hermitian matrices such as the weyl lidskii theorem and the hoffman wielandt theorem and those for generalized eigenspaces are counterparts of the celebrated davis kahan sin 0 sin 20 theorems for the eigenspace variations of hermitian matrices the paper consists of two parts part i is for generalized eigenvalue perturbations while part ii deals with generalized eigenspace perturbations

on the determination of the optimal pole position of laguerre filters as is known in the literature at each stationary point of the squared error se curve of a laguerre filter at least one of a pair of certain laguerre coefficients weights vanishes the author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the laguerre filter the knowledge of these derivatives makes possible the computation of high order approximations to the coefficients in question such as truncated taylor series and pade approximants the zeros of these approximations are usually good estimates of the location of the stationary points of the se curve nearer to the center of the approximation in this way the position of these stationary points in particular local minima can be estimated without resorting to a numerical search algorithm both continuous time and discrete time laguerre filters are discussed excited either by an impulse or by an arbitrary signal the authors illustrate the main results of the paper with a numerical example

brief paper frequency domain identification an algorithm based on an adaptive rational orthogonal system this paper presents a new adaptive algorithm for frequency domain identification the algorithm is related to the rational orthogonal system takenaka malmquist system this work is based on an adaptive decomposition algorithm previously proposed for decomposing the hardy space functions in which a greedy sequence is obtained according to the maximal selection criterion we modify the algorithm through necessary changes for system identification

estimation of model quality this paper provides an introduction to recent work on the problem of quantifying errors in the estimation of models for dynamic systems this is a very large field we therefore concentrate on approaches that have been motivated by the need for reliable models for control system design this will involve a discussion of efforts that go under the titles of estimation in th worst case estimation estimation in l1 and stochastic embedding of undermodelling a central theme of this survey is to examine these new methods with reference to the classic bias variance tradeoff in model structure selection

the perturbation bounds for eigenspaces of a definite matrix pair leta andb be hermitian matrices the matrix pair a b is called definite pair and the corresponding eigenvalue problem ax bx is definite if c a b equiv mathop min limits left x right 1 x h a ib x 0 the perturbation bounds for eigenspaces of a definite pair on every unitary invariant matrix norm were obtained by imposing additional restrictions on the location of the generalized eigenvalues thus it gives a positive answer for an open question proposed by stewart 7 the famous davis kahan sin theorems and sin 2 theorem 2 can also be deduced from the present results

the sample complexity of worst case identification of fir linear systems we consider the problem of identification of linear systems in the presence of measurement noise which is unknown but bounded in magnitude by some 0 we focus on the case of linear systems with a finite impulse response it is known that the optimal identification error is related within a factor of 2 to the diameter of a so called uncertainty set and that the latter diameter is upper bounded by 2 if a sufficiently long identification experiment is performed we establish that for any k 1 the minimal length of an identification experiment that is guaranteed to lead to a diameter bounded by 2k behaves like 2nf 1k when n is large where n is the length of the impulse response and is a positive function known in closed form while the framework is entirely deterministic our results are proved using probabilistic tools

recovery of functions by interpolation and sampling 1 introductionthe idea of recovering an element of a normed space from a sequenceof values of linear functionals is one that has received much study recentlyand which has a number of applications in for example systems theoryand signal processing 3 11 in many situations one is given a finite set ofwxmeasurements from which to construct an approximation to some un known function that is one hopes that given a sequence of linearfunctionals f

a unifying construction of orthonormal bases for system identification this paper develops a general and very simple construction for complete orthonormal bases for system identification this construction provides a unifying formulation of many previously studied orthonormal bases since the common fir and recently popular laguerre and two parameter kautz model structures are restrictive special cases of the construction presented here however in contrast to these special cases the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided

on the uniform approximation of discrete time systems by generalized fourier series in this paper model sets for linear time invariant discrete time systems spanned by fixed orthonormal bases are studied it is shown that the fourier series of the system transfer function with respect to these bases converges uniformly on the unit circle if the frequency response of the system is dini lipschitz continuous

algorithms for identification in h with unequally spaced function measurements abstract worst case identification in h is considered in the situation in which corrupted frequency response measurements are available at an arbitrary set of frequencies two new classes of algorithms are presented one yields polynomial models directly the other is a two stage algorithm producing rational models each has improved convergence rates for the class of exponentially stable discrete time systems with errors typically o e o r for arbitrarily large r where e is the noise level and is the maximum spacing between identification points a numerical example is given

identification of rational approximate models in h sup spl infin using generalized orthonormal basis robust identification with fir models fails to be successful when the number of coefficients to be estimated becomes large caused by lightly damped modes of the plant or poles very close to the unit circle the paper presents a two stage algorithm to obtain a low order approximate model in frequency domain in a generalized orthonormal basis with guaranteed h sup spl infin error bound for deterministic linear time invariant stable systems the first stage being an l sup spl infin rational approximation and the second nonlinear step being an h sup spl infin rational approximation

identification in h using pick s interpolation the problem of system identification in h is studied using the pick interpolation theorem a tuned nonlinear interpolation algorithm is proposed and the resulting error bound in h norm is derived an example is used to illustrate the use of the interpolation algorithm

h sub spl infin identification and model quality evaluation set membership h sub spl infin identification is investigated using time domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors the problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error called radius of information is solved for classes of models affine in the parameters the radius of information is obtained as function of the h sub spl infin norm of the unmodeled dynamics a method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics thus allowing the actual evaluation of the radius of information the radius represents a measure of the predictive ability of the considered class of models and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part the effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection

on perturbations of matrix pencils with real spectra ii a well known result on spectral variation of a hermitian matrix due to mirsky is the following let a and a be two n x n hermitian matrices and let 1 n and 1 n be their eigenvalues arranged in ascending order then diag 1 1 n n a a for any unitarily invariant norm in this paper we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra the much studied case of definite pencils is included in this