digital optimal control of continuous time systems with control delay abstract this paper solves the digital stationary optimal control problem in the case of scalar linear stochastic continuous time systems with control delay quadratic integral criteria complete state information and constant sampling periods by transforming the problem to an equivalent discrete time one without control delay expressions are given for the eigenvalues of the control system and the parameters of the feedback matrix the influence of the sampling period on the cost is investigated for different values of the control delay by means of some examples

chebyshev hankel matrices and the splitting approach for centrosymmetric toeplitz plus hankel matrices abstract centrosymmetric toeplitz plus hankel matrices are investigated on the basis of their splitting property which is their similarity to the direct sum of two special toeplitz plus hankel matrices these matrices can be considered as hankel matrices moment matrices in bases of chebyshev polynomials and are called chebyshev hankel matrices chebyshev hankel matrices have similar properties like hankel matrices this concerns inversion formulas and fast algorithms a superfast algorithm for solving chebyshev hankel and centrosymmetric toeplitz plus hankel systems is presented that is based on real trigonometric transforms the main tool of investigation is the interpretation of chebyshev hankel matrices as matrices of restricted multiplication operators with respect to chebyshev bases

statistical and stabilizability properties of equivalent discrete time systems with stochastic parameters this paper considers the influence of the statistics of a scalar continuous time system with white stochastic parameters on the statistics the correlation and the stabilizability of the corresponding scalar equivalent discrete time system by means of numerical examples some insight into the behaviour of the equivalent discrete time system is given furthermore these examples illustrate the crucial influence of the correlation between the state and control dependent noise of the continuous time system on the stabilizability of the equivalent discrete time system

stability and stabilizability of chemical reactors modelled with stochastic parameters abstract chemical reactors are considered where unknown parameter variations are model led by stochastic parameters the continuous time process is transformed to an equivalent discrete time system with stochastic parameters which is a natural approach in the context of digital control making the analysis much easier a stabilizability test for this discrete time model is used to analyse three cases from the chemical engineering literature it is shown that stability in a mean sense is too weak from an engineering point of view one should study stability at least in a mean square sense which is the approach given here

explicit solutions of the discrete time lyapunov matrix equation and kalman yakubovich equations a general solution for the nonsquare nonsymmetric lyapunov matrix equation in a canonical form is presented the solution is shown to be a toeplitz matrix which may be calculated using the backwards levinson algorithm this solution is then applied to the kalman yakubovich equations to derive a method for generating strictly positive real functions via the positive real lemma this latter result has an application in system identification

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

recursive solution of cauchy vandermonde systems of equations abstract recursive fast algorithms for the solution of linear systems ax b the coefficient matrix of which consists of a cauchy and a vandermonde matrix part are presented

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

generalized inversion of finite rank hankel and toeplitz operators with rational matrix symbols abstract the goal of the paper is a generalized inversion of finite rank hankel operators and hankel or toeplitz operators with block matrices having finitely many rows to attain it a left coprime fractional factorization of a strictly proper rational matrix function and the bezout equation are used generalized inverses of these operators and generating functions for the inverses are explicitly constructed in terms of the fractional factorization

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

a new algorithm for solving toeplitz systems of equations abstract we present some recurrences that are the basis for an algorithm to invert an n n toeplitz system of linear equations with computational complexity o n log 2 n the recurrences used are closely related to the zohar trench and bareiss algorithms but do not have any obvious connection with other asymptotically fast algorithms for the inversion of toeplitz systems

linear complexity parallel algorithms for linear systems of equations with recursive structure abstract a method of derivation of parallel algorithms for n 1 n 1 matrices with recursive structure is presented and applied to toeplitz hankel and other toeplitz like matrices the derived algorithms executed on o n parallel processors require o n arithmetic operations per processor

a generalization of the levinson algorithm for hermitian toeplitz matrices with any rank profile the paper describes a recursive algorithm for solving hermitian toeplitz systems of linear equations without any restriction on the ranks of their nested toeplitz subsystems such a general algorithm is needed e g to obtain the eigenfilters for signal processing applications or to compute the inverse of a nondefinite toeplitz matrix the regular portion of the algorithm is made of the classical levinson recursion the singular portion requires solving some well defined systems of linear equations with gradient structure the dimension of each of these sytems equals the amplitude of the corresponding singularity

iterative methods for discrete nonlinear riemann hilbert problems abstract let d denote the complex unit disk t d and let f t r 2 r be a given function the paper presents iterative methods for the computation of functions w u iv which are holomorphic in d and satisfy the boundary relation f t u t v t 0 for all t t it is shown that an appropriate discretization of this boundary value problem can be obtained by replacing the class of holomorphic functions with the set of polynomials of degree not exceeding n and imposing the boundary condition at a grid of 2n uniformly distributed points on the circle t the proposed iterative methods for the solution of the discrete as well as the nondiscrete problems converge quadratically in a neighborhood of the solution error estimates for the iterative solutions are given in the scale of the sobolev spaces wk2

time delay estimation with unknown spatially correlated gaussian noise the problem of estimating the difference in arrival times of a non gaussian signal at two spatially separated sensors is considered the signal is assumed to be corrupted by spatially correlated gaussian noises of unknown cross correlation the author proposes and analyzes two new classes of methods for time delay estimation based on higher order statistics the proposed methods are conceptually very similar to the traditional cross correlation based techniques in that the proposed criteria peak at a lag value equalizing true delay since the proposed methods are based upon higher order cumulant statistics of the data they result in estimators that remain unbiased in the presence of gaussian noise

time domain approaches to quadratic phase coupling estimation bicoherence is a quantity used to estimate the contribution of second order nonlinearity to the power in bifrequencies the conventional approach to the problem uses second and third order periodograms for bicoherence estimation time domain approaches that use autocorrelation and third order cumulant samples or their estimates are developed these techniques are suitable for use in situations where high resolution approaches are required for power spectrum and bispectrum estimation

riemann roch for homotopy invariant k theory and gysin morphisms abstract we prove the riemann roch theorem for homotopy invariant k theory and projective local complete intersection morphisms between finite dimensional noetherian schemes without smoothness assumptions we also prove a new riemann roch theorem for the relative cohomology of a morphism in order to do so we construct and characterize new gysin morphisms for regular immersions between cohomologies represented by spectra examples include homotopy invariant k theory motivic cohomology their arithmetic counterparts real absolute hodge and deligne beilinson cohomology rigid syntomic cohomology mixed weil cohomologies and we use this construction to prove a motivic version of the riemann roch

recursive blind symbol estimation of convolutionally coded cochannel signals a recursive blind equalizer is presented that directly estimates the transmitted symbols of multiple cochannel signals in the presence of isi the algorithm exploits shift structure present in the data model and the finite alphabet property of the signals the proposed method possesses a separation property that allows the symbol sequences for each user to be estimated independently of the others problematic issues surrounding unknown and mismatched channel lengths for the cochannel users can be handled effectively in the recursive equalizer additionally if the cochannel signals are encoded prior to transmission we show how the code structure can be incorporated into the recursive equalizer to improve its performance

the group inverse of the transformation j x ax xb abstract the group inverse j of the sylvester transformation j x ax xb is provided that it exists represented in polynomial form j y ij c ij a i yb j in terms of the minimal polynomials of a and b in one of the representations the coefficient matrix c ij is expressed with the help of a new class of derived hankel matrices

inversion des matrices de hankel abstract hankel determinants can be viewed as special schur symmetric functions this provides without computations of determinants or matrices most of the algebra of hankel determinants and explains their links with other classical fields

identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

parallel and superfast algorithms for hankel systems of equations utilizing kernel structure properties a unified construction of hankel matrix inversion algorithms is presented three types of algorithms are obtained 1 o n 2 complexity levinson type 2 o n parallel complexity schur type and 3 o n log2 n complexity asymptotically fast ones all algorithms work without additional assumption like strong nonsingularity

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

lyapunov equations for companion matrices abstract matrix equations of the form c a x xc t b y where ca and cb are companion matrices are considered in a first step 1 is reduced to an equation for which the solution is hankel and the right side has rank 2 at most in a second step a solvability condition and a general solution are given in terms of the polynomials a b and the solution of some polynomial congruence an application to resultant matrix equations is included

ica in signals with multiplicative noise independent component analysis ica has been shown in the last few years to be a very useful tool in blind separation of sources and feature extraction however at least in its simpler form its utility is reduced to the case that the outputs are linear mixtures of independent sources this excludes signals with multiplicative noise in this paper ica is extended to this situation in order to do this the special structure that appears in this new model is first studied and then the multiplicative ica method is designed such that it uses this structure to find the mixture of the sources in the noisy environment the local and global convergence properties of the method are also studied and its performance compared with standard ica methods

hankel matrices generated by the markov parameters of rational functions abstract finite hankel matrices s i j are considered for which s i are the markov parameters of a given rational function p a the problems of inversion and kernel description are reduced to the problem of solving some polynomial congruences in terms of p and a an application to hankel matrices of the form y t c i j a x where c a is a companion matrix is included

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

borel moore motivic homology and weight structure on mixed motives by defining and studying functorial properties of the borel moore motivic homology we identify the heart of bondarko hebert s weight structure on beilinson motives with corti hanamura s category of chow motives over a base therefore answering a question of bondarko

bezoutians and intertwining matrices abstract using the notion of an intertwining matrix introduced in a previous paper the authors show that the class of all n by n bezoutians compatible with a nonzero polynomial of degree n may be characterized by an intertwining relation as well as by four other conditions formulated in terms of the structure of these matrices

lyapunov bezout and hankel abstract given a polynomial f of degree n we denote by c its companion matrix and by s the truncated shift operator of order n we consider lyapunov type equations of the form x sxc w and x cxs w we derive some properties of these equations which make it possible to characterize bezoutian matrices as solutions of the first equation with suitable right hand sides w similarly for hankel and the second equation and to write down explicit expressions for these solutions this yields explicit factorization formulae for polynomials in c for the schur cohn matrix and for matrices satisfying certain intertwining relations as well as for bezoutian matrices

effective channel order estimation based on nullspace structure and exponential fit the selection criteria for the order of a single input multiple output simo channel generally use the singular values of the estimated least squares matrix using these values ignores important information that can be obtained from the nullspace of the least squares matrix the nullspace has a structured basis that can be utilized to quantify the quality of channel coefficient estimates these quantities cluster in the nullspace and spread in the signal space when compared to the singular values a simple exponential curve fit is used to further improve the estimate of the effective channel order the new criterion outperforms other known criteria in a wide variety of scenarios at both high and low snr

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

stabilization of linear systems by noise it is proved that the biggest lyapunov number lambda max of the system dot x a f t x where a is a fixed d times d matrix and f t is a zero mean strictly stationary matrix valued stochastic process satisfies 1 d trace a leqq lambda max on the other hand for each varepsilon 0 there is a process f t for which lambda max leqq 1 d trace a varepsilon in particular the system dot x ax can be stabilized by zero mean stationary parameter noise if and only if trace a 0 the stabilization can be accomplished by a one dimensional noise source the results carry over to the case where a is a stationary process they are also true for f t white noise

control of randomly varying systems with prescribed degree of stability the control of linear discrete time systems with stochastic parameter matrices is discussed two control techniques are particularly used infinite horizon and finite moving horizon optimal regulators it is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes in this way the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems

displacement structure of generalized inverse matrices abstract it is shown that matrices with a uv displacement structure possess generalized inverses with a vu displacement structure estimations for the displacement rank of the generalized inverses are presented the results apply to matrices of toeplitz vandermonde and cauchy type and provide formulas for generalized inverses which are important for fast algorithms

note on products of bezoutians and hankel matrices abstract a quantitative theorem due to fiedler and ptak on products of bezoutians and their inverses is extended to a more general case using as the main tool an alternative to fiedler s assertion on the quasidirect decomposition of hankel matrices

the singular value decomposition and long and short spaces of noisy matrices using geometrical algebraic and statistical arguments it is clarified why and when the singular value decomposition is successful in so called subspace methods first the concepts of long and short spaces are introduced and a fundamental asymmetry in the consistency properties of the estimates is discussed the model which is associated with the short space can be estimated consistently but the estimates of the original data which follow from the long space are always inconsistent an expression is found for the asymptotic bias in terms of canonical angles which can be estimated from the data this allows all equivalent reconstructions of the original signals to be described as a matrix ball the center of which is the minimum variance estimate remarkably the canonical angles also appear in the optimal weighting that is used in weighted subspace fitting approaches the results are illustrated with a numerical simulation a number of examples are discussed

the equivalent discrete time optimal control problem for continuous time systems with stochastic parameters this paper considers the transformation of the digital optimal control problem to an equivalent discrete time optimal control problem for linear continuous time systems with continuous time white stochastic parameters and additive continuous time white noise the observations available at the sampling instants are in general non linear and corrupted by discrete time noise the equivalent discrete time system has white stochastic parameters expressions are derived for the first and second moments of these parameters and for the cost criterion parameters which are explicit in the parameters and the statistics of the continuous time system

recursive relations for block hankel and toeplitz systems part ii dual recursions abstract the recursive relations given in part i of this report can be interpreted as recursions for the denominators of matrix pade approximants in this part we shall give dual relations for the corresponding numerators and residuals

brief paper optimal reduced order compensation of time varying discrete time systems with deterministic and white parameters the finite horizon optimal compensation problem is considered in the case of linear time varying discrete time systems with deterministic and white stochastic parameters and quadratic criteria the dimensions of the compensator are a priori fixed and may be time varying also the dimensions of the system may be time varying strengthened discrete time optimal projection equations sdope are developed which within the class of minimal compensators are equivalent to the first order necessary optimality conditions based on the sdope and their associated boundary conditions two numerical algorithms are presented to solve the two point boundary value problem one is a homotopy algorithm while the second iterates the sdope repeatedly forward and backward in time the latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation riccati equations associated with the full order problem for systems with deterministic parameters the algorithms are illustrated with a numerical example the case of systems with deterministic parameters will be treated as a special case of systems with white parameters

hankel matrices and the infinite companion abstract a formula of barnett type relating the bezoutian b f g to the hankel matrix h g f is extended to rectangular bezoutians the proof is based on an interesting relation between the family of all hankel matrices corresponding to the markov parameters of g f and the infinite companion matrix corresponding to f

split algorithms for hermitian toeplitz matrices with arbitrary rank profile abstract split algorithms for toeplitz matrices exploit besides the toeplitz structure additional symmetry properties to reduce the number of operations in this paper split levinson and schur algorithms for hermitian toeplitz matrices are presented that work in contrast to previous algorithms without additional conditions like strong nonsingularity the main contribution is the generalization of the split levinson type algorithms of b krishna h krishna and h krishna s morgera to general nonsingular hermitian toeplitz matrices furthermore a schur type counterpart of this algorithm is presented that is also new in the strongly nonsingular case some auxiliary considerations concerning the kernel structure of hermitian toeplitz matrices might be of independent interest

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

the optimal projection equations for fixed order sampled data dynamic compensation with computation delay for an lqg type sampled data regulator problem which accounts for computational delay and utilizes an averaging a d device the equivalent discrete time problem is shown to be of increased order due to the inclusion of delayed measurement states the optimal projection equations for reduced order discrete time compensation are applied to the augmented problem to characterize low order controllers the design results are illustrated on a tenth order flexible beam example

vandermonde factorization and canonical representations of block hankel matrices abstract we study to which extent well known facts concerning vandermonde factorization or canonical representation of scalar hankel matrices transfer to block hankel matrices with p q blocks it is shown that nonsingular block hankel matrices can be factored like in the scalar case into nonconfluent vandermonde matrices and that the theorem on full rank factorization of arbitrary hankel matrices transfers in a weak version to the 2 2 block case but not to larger block sizes in general the minimal rank of a vandermonde factorization both with finite nodes and affine is described in terms of the hankel matrix the main tools are realization partial realization and moebius transformations

covariance sequence approximation for parametric spectrum modeling parametric methods of spectrum analysis are founded on finite dimensional models for covariance sequences rational spectrum approximants for continuous spectra are based on autoregressive ar moving average ma or autoregressive moving average arma models for covariance sequences line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences in this paper we make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes frequencies and damping factors the associated modal decomposition is appropriate for both continuous and discrete components of the spectrum the domain of attraction for the decomposition includes arma sequences harmonically or nonharmonically related sinusoids damped sinusoids white noise and linear combinations of these the parametric spectrum analysis problem now becomes one of identifying mode parameters this we achieve by solving two modified least squares problems numerical results are presented to illustrate the identification of mode parameters and corresponding spectra from finite records of perfect and estimated covariance sequences the results for sinusoids and sinusoids in white noise are interpreted in terms of in phase and quadrature effects attributable to the finite record length

bispectral analysis and model validation of texture images statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian and or asymmetric in this paper higher than second order statistics are used to derive and implement 2 d gaussianity linearity and spatial reversibility tests that validate the respective modeling assumptions the nonredundant region of the 2 d bispectrum is correctly defined and proven a consistent parameter estimator for nonminimum phase asymmetric noncausal 2 d arma models is derived by minimizing a quadratic error polyspectrum matching criterion simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported

the lanczos algorithm and hankel matrix factorization abstract we explore the connections between the lanczos algorithm for matrix tridiagonalization and two fast algorithms for hankel matrix factorization we show how the asymmetric lanczos process is related to the berlekamp massey algorithm and how the symmetrized lanczos process is related to the phillips algorithm we also discuss conditions under which the analysis of phillips applies

a new algorithm for computing orthogonal polynomials the aim of this paper is to present an algorithm for computing orthogonal polynomials the fast fourier transform completes the connection given by draux between the three term recurrence relationship and the euclidian algorithm applications to hankel systems and numerical examples illustrate our purpose

on inversion of toeplitz and close to toeplitz matrices abstract it is proved that three columns of an inverse of a scalar toeplitz matrix when properly chosen are always enough to reconstruct it a parametrization of invertible toeplitz matrices in terms of the first and a combination of two consecutive columns of the inverse matrix is also given

kernel structure of block hankel and toeplitz matrices and partial realization abstract the kernel structure of block hankel and toeplitz matrices is studied this leads to the concept of a fundamental system which is basic in the theory and provides in particular a natural background for the partial realization problem

mixed weil cohomologies abstract we define for a regular scheme s and a given field of characteristic zero k the notion of k linear mixed weil cohomology on smooth s schemes by a simple set of properties mainly nisnevich descent homotopy invariance stability which means that the cohomology of g m behaves correctly and kunneth formula we prove that any mixed weil cohomology defined on smooth s schemes induces a symmetric monoidal realization of some suitable triangulated category of motives over s to the derived category of the field k this implies a finiteness theorem and a poincare duality theorem for such a cohomology with respect to smooth and projective s schemes which can be extended to smooth s schemes when s is the spectrum of a perfect field this formalism also provides a convenient tool to understand the comparison of such cohomology theories

an output error method for reduced order controller design an efficient computational technique is presented for the design of reduced order controllers for linear discrete time systems the technique is based on the minimization of the output error between the closed loop system and a specified reference model

inverse problems for hankel and toeplitz matrices abstract the problem is considered how to construct a toeplitz or hankel matrix a from one or two equations of the form au g the general solution is described explicitly special cases are inverse spectral problems for hankel and toeplitz matrices and problems from the theory of orthogonal polynomials

optimal projection equations for discrete time fixed order dynamic compensation of linear systems with multiplicative white noise the optimal projection equations for discrete time reduced order dynamic compensation are generalized to include the effects of state control and measurement dependent noise in addition the discrete time static output feedback problem with multiplicative disturbances is considered for both problems the design equations are presented in a concise unified manner to facilitate their accessibility for developing numerical algorithms for practical applications

resultant matrices and inversion of bezoutians abstract the goal of this paper is to construct inverses of toeplitz and hankel bezoutians we obtain quite explicit formulas which are also specified to cases where the bezoutians possess additional symmetries the construction relies on a result about the nullspace of generalized resultant matrices which can be described by means of the solutions of corresponding bezout equations

on recursiveness and related topics in linear systems a decomposition of matrix formal power series linear systems is developed the interconnections between formal power series realization pade approximation recursiveness berlekamp massey algorithm feedback interconnections matrix linear fractional representations matrix continued fractions and the matrix euclidean algorithm are thereby revealed

on the use of kernel structure for blind equalization the mathematical theory of kernel null space structure of hankel and hankel like matrices is applied to the problem of blind equalization of cochannel signals this approach provides a new perspective on the blind equalization problem and gives insights into the identifiability conditions already presented in the literature an algorithm is presented that tracks the exact null space of the symbol matrix even in the presence of noise this work exploits the shift structure in the oversampled channel output and the finite alphabet property of the signals previously these two properties were used independently in a two step equalize then separate process a contribution of the new approach is that is allows simultaneous exploitation of both the shift structure and the finite alphabet property of the signals

blind separation of synchronous co channel digital signals using an antenna array i algorithms we propose a maximum likelihood ml approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site the spatial response of the array is assumed to be known imprecisely or unknown we exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal uniqueness of the estimates is established for bpsk signals we introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner computationally efficient algorithms for both block and recursive estimation of the signals are presented this new approach is applicable to an unknown array geometry and propagation environment which is particularly useful in wireless communication systems simulation results demonstrate its promising performance

hankel matrices of finite rank with applications to signal processing and polynomials abstract it is shown that certain sequences of hankel matrices of finite rank obtained from a given sequence of complex numbers and powers of companion matrices are closely related this relation is established by investigating the algebraic properties of combinations of polynomial multiples of powers of complex numbers among many applications these properties are used to construct polynomials with zeros being a function of the zeros of given polynomials for example hankel matrices of finite rank are used to develop a method for computing the least common multiple of a finite number of polynomials without factoring them or computing a polynomial whose zeros are the product of the zeros of two polynomials a method for computing a factor of the characteristic polynomial of a given matrix is also presented and is established by forming certain types of hankel matrices whose entries are generated from linear combinations of powers of zeros of its characteristic polynomial applications of these ideas to signal processing and computational linear algebra are also given