partial eigenvalue assignment problem of high order control systems using orthogonality relations in this paper we present an explicit solution to the partial eigenvalue assignment problem of high order control system using orthogonality relations between eigenvectors of the matrix polynomial our solution can be implemented with only a partial knowledge of the spectrum and the corresponding left eigenvectors of the matrix polynomial we show that the number of eigenvalues and eigenvectors that need to remain unchanged will not affected by feedback a numerical example is given to illustrate the applicability and the practical usefulness of the proposed method

gmres for the differentiation operator we investigate using the gmres method with the differentiation operator this operator is unbounded and thus does not fall into the framework of existing krylov subspace theory we establish conditions under which a function can be approximated by its own derivatives in a domain of the complex plane these conditions are used to determine when gmres converges this algorithm outperforms traditional quadrature schemes for a large class of highly oscillatory integrals even when the kernel of oscillations is unknown

relaxation strategies for nested krylov methods this paper studies computational aspects of krylov methods for solving linear systems where the matrix vector products dominate the cost of the solution process because they have to be computed via an expensive approximation procedure in recent years so called relaxation strategies for tuning the precision of the matrix vector multiplications in krylov methods have proved to be effective for a range of problems in this paper we will argue that the gain obtained from such strategies is often limited another important strategy for reducing the work in the matrix vector products is preconditioning the krylov method by another iterative krylov method flexible krylov methods are krylov methods designed for this situation we combine these two approaches for reducing the work in the matrix vector products specifically we present strategies for choosing the precision of the matrix vector products in several flexible krylov methods as well as for choosing the accuracy of the variable preconditioner such that the overall method is as efficient as possible we will illustrate this computational scheme with a schur complement system that arises in the modeling of global ocean circulation

a parallel algorithm for the sylvester observer equation we present a new algorithm for solving the sylvester observer equation arising in the context of the luenberger observer the algorithm embodies two main computational phases the solution of several independent equation systems and a series of matrix matrix multiplications the algorithm is thus well suited for parallel and high performance computing by reducing the coefficient matrix a to lower hessenberg form one can implement the algorithm efficiently with few floating point operations and little workspace the algorithm has been successfully implemented on a cray c90 a comparison both theoretical and experimental has been made with the well known hessenberg schur algorithm which solves an arbitrary sylvester equation our theoretical analysis and experimental results confirm the superiority of the proposed algorithm both in efficiency and speed over the hessenberg schur algorithm

solving shifted linear systems with restarted gmres augmented with error approximations abstract in this paper we investigate a variant of the restarted gmres method for solving a series of large sparse linear systems restarting is carried out by augmenting krylov subspaces with some recently generated error approximations from the seed system the method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix vector multiplication per iteration compared with solving each added linear system separately the advantage of the new scheme is to lower down the overall cost of solving all added linear systems numerical experiments illustrate the efficiency of the acceleration strategy

incomplete partial fractions for parallel evaluation of rational matrix functions abstract frequently one needs to evaluate expressions of the form p a 1q a b where a r n n b r n and p and q are polynomials with degree q degree p and such that no zero of p is an eigenvalue of a algorithms based on the partial fraction representation of q p when evaluating p a 1 q a b lend themselves well to implementation on a parallel computer but might yield poor accuracy we discuss how to determine an incomplete partial fraction representation of q p which allows parallel computation while retaining high accuracy

deflated gmres for systems with multiple shifts and multiple right hand sides abstract we consider solution of multiply shifted systems of nonsymmetric linear equations possibly also with multiple right hand sides first for a single right hand side the matrix is shifted by several multiples of the identity such problems arise in a number of applications including lattice quantum chromodynamics where the matrices are complex and non hermitian some krylov iterative methods such as gmres and bicgstab have been used to solve multiply shifted systems for about the cost of solving just one system restarted gmres can be improved by deflating eigenvalues for matrices that have a few small eigenvalues we show that a particular deflated method gmres dr can be applied to multiply shifted systems in quantum chromodynamics it is common to have multiple right hand sides with multiple shifts for each right hand side we develop a method that efficiently solves the multiple right hand sides by using a deflated version of gmres and yet keeps costs for all of the multiply shifted systems close to those for one shift an example is given showing this can be extremely effective with a quantum chromodynamics matrix

a hybrid block gmres method for nonsymmetric systems with multiple right hand sides the block gmres bgmres method is a natural generalization of the gmres algorithm for solving large non symmetric systems with multiple right hand sides unfortunately its cost increases significantly per iteration frequently rendering the method impractical in this paper we propose a hybrid block gmres method which offers significant performance improvements over bgmres this method uses the matrix polynomial obtained in the course of a bgmres step and combines the advantages of the block approach with those of successful hybrid methods we discuss the properties and several implementation variants of the method and report results from numerical experiments we also describe how to use these techniques in order to solve multiply shifted systems with multiple right hand sides

computational methods for linear matrix equations given the square matrices a b d e and the matrix c of conforming dimensions we consider the linear matrix equation a mathbf x e d mathbf x b c in the unknown matrix mathbf x our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing

an optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures the partial quadratic eigenvalue assignment problem pqevap concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged the problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems the solution of this problem requires computations of a pair of feedback matrices for practical effectiveness these feedback matrices must be computed in such a way that their norms and the condition number of the closed loop eigenvector matrix are as small as possible these considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem mnpqevap and the robust partial quadratic eigenvalue assignment problem rpqevap respectively in this paper we propose new optimization based algorithms for solving these problems the problems are solved directly in a second order setting without resorting to a standard first order formulation so as to avoid the inversion of a possibly ill conditioned matrix and the loss of exploitable structures of the original model the algorithms require the knowledge of only the open loop eigenvalues to be replaced and their corresponding eigenvectors the remaining open loop eigenvalues and their corresponding eigenvectors are kept unchanged the invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result furthermore the gradient formulas needed to solve the problems by using the quasi newton optimization technique employed are computed in terms of the known quantities only above all the proposed methods do not require the reduction of the model order or the order of the controller even when the underlying finite element model has a very large degree of freedom these attractive features coupled with minimal computational requirements such as solutions of small diagonal sylvester equations make the proposed algorithms ideally suited for application to large real life structures numerical results show significant improvement in feedback norms and in the condition number of the closed loop system also the closed loop eigenvalues have acceptable accuracy

solution of generalized shifted linear systems with complex symmetric matrices we develop the shifted cocg method r takayama t hoshi t sogabe s l zhang t fujiwara linear algebraic calculation of green s function for large scale electronic structure theory phys rev b 73 165108 2006 1 9 and the shifted wqmr method t sogabe t hoshi s l zhang t fujiwara on a weighted quasi residual minimization strategy of the qmr method for solving complex symmetric shifted linear systems electron trans numer anal 31 2008 126 140 for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory the complex symmetric lanczos process with a suitable bilinear form plays an important role in the development of the methods the numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved

functional observer for linear parameter varying systems with application to diagnosis of pem fuel cell this paper is a contribution to the problem of functional observers for linear parameter varying systems the goal is twofold first we propose an extension of some results of literature on functional observers established originally for linear systems to systems the design of these observers are based on linear interpolation principle according to each parameter besides sufficient conditions for asymptotic convergence are expressed in terms of linear matrix inequalities easily tractable by convex optimisation techniques second we show how this new result can be used to investigate the problem of diagnosis for proton electrolyte membrane fuel cell more precisely we deal with the problem of flooding considered as an important issue for water management inside the fuel cell finally simulation results are given in order to highlight the performances of the proposed approach

an algorithm to assign eigenvalues in a hessenberg matrix single input case we propose a conceptually simple algorithm to assign eigenvalues in a hessenberg matrix the method is based on the evaluation of a simple recursive relation and it is extremely easy to program on a computer numerical experiments compare favorably to those of other methods recently proposed for the problem

a new block algorithm for full rank solution of the sylvester observer equation a new block algorithm for computing a full rank solution of the sylvester observer equation arising in state estimation is proposed the major computational kernels of this algorithm are 1 solutions of standard sylvester equations in each case of which one of the matrices is of much smaller order than that of the system matrix and furthermore this small matrix can be chosen arbitrarily and 2 orthogonal reduction of small order matrices there are numerically stable algorithms for performing these tasks including the krylov subspace methods for solving large and sparse sylvester equations the proposed algorithm is also rich in level 3 basic linear algebra subroutine blas 3 computations and is thus suitable for high performance computing furthermore the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem

restarted weighted full orthogonalization method for shifted linear systems it is known that the restarted full orthogonalization method fom outperforms the restarted generalized minimum residual method gmres in several circumstances for solving shifted linear systems when the shifts are handled simultaneously on the basis of the weighted arnoldi process a weighted version of the restarted shifted fom is proposed which can provide accelerating convergence rate with respect to the number of restarts in the cases where our hybrid algorithm needs less enough number of restarts to converge than the restarted shifted fom the associated cpu consuming time is also reduced as shown by the numerical experiments moreover our algorithm is able to solve certain shifted systems which the restarted shifted fom cannot handle sometimes

resonant enhancement of anderson localization analytical approach we study localization properties of the eigenstates and wave transport in a one dimensional system consisting of a set of barriers and or wells of fixed thickness and random heights the inherent peculiarity of the system resulting in the enhanced anderson localization is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between the wells and or barriers our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them we examine how the transport properties of finite samples can be described in terms of this length it is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model in spite of the presence of resonances that cannot be described by conventional theories all our results are illustrated with numerical data manifesting an excellent agreement with the theory

disturbance decoupling using constrained sylvester equations presents numerically efficient algorithms for the problem of disturbance decoupling with arbitrary pole placement using state feedback with or without disturbance measurement the problem is studied under conditions of generic solvability the main tool for the development of the proposed algorithm is the notion of constrained sylvester equations these equations follow naturally from the already existing geometric conditions for the same problem in the literature

linear and numerical linear algebra in control theory some research problems abstract this paper presents an informal survey of theoretical and computational aspects of three linear algebra problems arising in control theory namely the sylvester observer matrix equation the matrix eigenvalue assignment problem and the stability and stabilization of large second order systems difficulties are highlighted recent developments are mentioned some research problems in these areas which should be of interest to both linear algebraists and control theorists are described

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

parallel algorithms for certain matrix computations abstract the complexity of performing matrix computations such as solving a linear system inverting a nonsingular matrix or computing its rank has received a lot of attention by both the theory and the scientific computing communities in this paper we address some nonclassical matrix problems that find extensive applications notably in control theory more precisely we study the matrix equations ax xa t c and ax xb c the inverse of the eigenvalue problem called pole assignment and the problem of testing whether the matrix b ab a n 1 b has full row rank for these problems we show two kinds of pram algorithms on one side very fast i e polylog time algorithms and on the other side almost linear time and processor efficient algorithms in the latter case the algorithms rely on basic matrix computations that can be performed efficiently also on realistic machine models

closed form solutions to sylvester conjugate matrix equations some explicit closed form solutions of homogeneous and nonhomogeneous sylvester conjugate matrix equations are provided in this paper one of the solutions is expressed in terms of controllability matrices and observability matrices the proposed approach does not require all the coefficient matrices to be in any canonical forms and the solutions provide a significant degree of freedom which is represented by an arbitrarily chosen parameter matrix by specifying the solutions of the homogeneous sylvester conjugate equation some new expressions of the solutions of the normal sylvester normal sylvester conjugate and sylvester equations are given this fact reveals that the sylveter conjugate matrix equations are a more general class of some previously investigated matrix equations

a pole assignment algorithm for linear state feedback abstract a new algorithm for the pole assignment problem of a controllable time invariant linear multivariable system with linear state feedback is presented the resulting feedback matrix is a least squares solution and is robust in a loose sense the method is based on the controllability canonical staircase form and amounts to a new proof for the existence of a solution of the pole assignment problem illustrative examples are given

pole assignment via sylvester s equation it is shown that the pole assignment problem can be reduced to solving the linear matrix equations ax xa bg fx g successively for x and then f for almost any choice of g the result is a new pole assignment procedure and proof of the pole assignment theorem that should play an important role in both theoretical and practical applications

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

robustness in partial pole placement the robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined the projection procedure gives a reduced order pole assignment problem it is shown that the sensitivities of the assigned poles in the complete closed loop system are bounded in terms of the sensitivities of the assigned reduced order poles and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open loop poles if the assigned poles are well separated from the unaltered poles these bounds are expected to be tight the projection procedure is described in 3 and techniques for finding robust or insensitive solutions to the reduced order problem are given in 1 2

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

iterative system solvers for the frequency analysis of linear mechanical systems abstract the paper deals with the numerical treatment of the direct frequency domain dfd analysis of linear mechanical systems attention is mainly focused on the solution of the complex system of equations needed for each analyzed frequency strategies for transforming the system into the shifted form t i z d are proposed and discussed where is related to the frequency for two formulations of the shifted system the performance of some krylov sub space iterative solvers is tested and compared to that of a multi frontal direct method advantage is taken of the shifted form in solving simultaneously a large number of systems resulting from different values of the shift frequency numerical experiments on some prototype structural dynamics problems are reported the results shown demonstrate how the devised strategies for the iterative solution can outperform in many cases the direct solver

computation of minimal order state space realizations and observability indices using orthogonal transformations in this paper an algorithm is presented for obtaining a minimal order state space realization of a strictly proper rational function matrix the algorithm can also be used to compute the observability indices of any given state space system a controllable but unobservable state space realization of the given rational function matrix is first obtained by inspection the algorithm then performs a sequence of simple coordinate transformations on the state vector of the system the coordinate transformation matrices are orthogonal and are easily constructed from the system matrices each coordinate transformation operates on submatrices of the state space system matrices of lower dimension than the preceding one the sequence of coordinate transformations terminates after at most v 1 1 transformations where v 1 is the maximal observability index of the state space model the observability indices of the system are also determined at this time the transformed system matrices are obtained in a form wh

reduced order observers a new algorithm and proof this paper gives a new recursive algorithm to construct a reduced order observer with prescribed spectrum of a given observable system the method is based on the staircase form and implicitly gives a new proof for the existence of such reduced order observers

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

design of state feedback for large scale multivariable systems this note presents a general method which reduces the computational requirements in the state feedback design of large scale multivariable systems the given system is first transformed into a general block canonical form by using simple equivalent transformation the state feedback problem is then reformulated in terms of a sylvester equation finally the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively

the lanczos arnoldi algorithm and controllability we present methods for computing the controllable space of a linear dynamic system the methods are based on orthogonalizing krylov sequences and can use much less storage than other methods with little or no loss of numerical stability

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

the class number one problem for some non abelian normal cm fields of degree 48 we prove that there is precisely one normal cm field of degree 48 with class number one which has a normal cm subfield of degree 16 the narrow hilbert class field of q 5 101 with 3 2 5 1 0

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

a complete analytical solution to the equation ta ft lc and its applications in this note a complete analytical and restriction free solution with complete and explicit freedom of the matrix equation ta ft lc is proposed here a c is given and is observable and f is in the jordan form with arbitrary given eigenvalues this solution appears to be new because it can be applied directly to obtain significantly better solutions to the following three basic design problems 1 2 d system eigenvalue assignment 2 function observer design and 3 state feedback eigenstructure design as shown in this note

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

fast cg based methods for tikhonov phillips regularization tikhonov phillips regularization is one of the best known regularization methods for inverse problems a posteriori criteria for determining the regularization parameter alpha require solving a a alpha i x a y delta for different values of alpha we investigate two methods for accelerating the standard cg algorithm for solving the family of systems the first one utilizes a stopping criterion for the cg iterations which depends on alpha and delta the second method exploits the shifted structure of the linear systems which allows us to solve simultaneously for different values of alpha we present numerical experiments for three test problems which illustrate the practical efficiency of the new methods the experiments as well as theoretical considerations show that run times are accelerated by a factor of at least 3

shifted gmres for oscillatory integrals none of the existing methods for computing the oscillatory integral int a b f x rm e rm i omega g x rm d x achieve all of the following properties high asymptotic order stability avoiding deformation into the complex plane and insensitivity to oscillations in f we present a new method that satisfies these properties based on applying the gmres algorithm to a shifted linear differential operator

phase diagram of the random frequency oscillator the case of ornstein uhlenbeck noise abstract we study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an ornstein uhlenbeck noise this system undergoes a noise induced bifurcation when the amplitude of the noise grows the critical curve that separates the absorbing phase from an extended non equilibrium steady state corresponds to the vanishing of the lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy we derive various expressions for this lyapunov exponent by using different approximation schemes this allows us to study quantitatively the phase diagram of the random parametric oscillator

generalized lyapunov exponents of the random harmonic oscillator cumulant expansion approach the cumulant expansion is used to estimate generalized lyapunov exponents of the random frequency harmonic oscillator three stochastic processes are considered gaussian white noise ornstein uhlenbeck and poisson shot noise in some cases nontrivial numerical difficulties arise these are mostly solved by implementing an appropriate importance sampling monte carlo scheme we analyze the relation between random frequency oscillators and many particle systems with pairwise interactions like the lennard jones gas

arnoldi methods for large sylvester like observer matrix equations and an associated algorithm for partial spectrum assignment abstract we propose an arnoldi based numerical method for solving a sylvester type equation arising in the construction of the luenberger observer given an n n matrix a and an n m matrix g the method simultaneously constructs an m m hessenberg matrix h with a preassigned spectrum and an n m orthonormal matrix x such that ax xh g we consider the case when a is large and sparse so that the standard techniques such as the well known hessenberg schur method for solving a sylvester equation cannot be easily applied as a byproduct we propose an algorithm for the partial pole assignment problem for large matrices

bicr type methods for families of shifted linear systems the shifted linear systems with non hermitian matrices often arise from the numerical solutions for time dependent pdes computing the large scale eigenvalue problems control theory and so on in the present paper we develop two shifted variants of bicr type methods for solving such linear systems these variants of bicr type methods take advantage of the shifted structure so that the number of matrix vector multiplications and the number of inner products are the same as a single linear system finally extensive numerical examples are reported to illustrate the performance and effectiveness of the proposed methods

anderson localization as a parametric instability of the linear kicked oscillator we rigorously analyze the correspondence between the one dimensional standard anderson model and a related classical system the kicked oscillator with noisy frequency we show that the anderson localization corresponds to a parametric instability of the oscillator the localization length being related to the rate of exponential growth of the energy of the oscillator analytical expression for a weak disorder is obtained which is valid both inside the energy band and at the band edge

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

computational design techniques for reduced order compensators the authors propose two computational techniques for the pole placement problem using reduced order compensators computationally efficient algorithms are presented for the observer based compensator and the brasch pearson compensator the key tool for these algorithms is the concept of two coupled sylvester equations the solutions of which completely characterize the desired reduced order compensators

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

exploring multimodal data fusion through joint decompositions with flexible couplings a bayesian framework is proposed to define flexible coupling models for joint tensor decompositions of multiple datasets under this framework a natural formulation of the data fusion problem is to cast it in terms of a joint maximum a posteriori map estimator data driven scenarios of joint posterior distributions are provided including general gaussian priors and non gaussian coupling priors we present and discuss implementation issues of algorithms used to obtain the joint map estimator we also show how this framework can be adapted to tackle the problem of joint decompositions of large datasets in the case of a conditional gaussian coupling with a linear transformation we give theoretical bounds on the data fusion performance using the bayesian cramer rao bound simulations are reported for hybrid coupling models ranging from simple additive gaussian models to gamma type models with positive variables and to the coupling of data sets which are inherently of different size due to different resolution of the measurement devices

the class number one problem for some non abelian normal cm fields let n be a non abelian normal cm eld of degree 4p p any odd prime note that the galois group of n is either the dicyclic group of order 4p or the dihedral group of order 4p we prove that the relative class number of a dicyclic cm eld of degree 4p is always greater then one then we determine all the dihedral cm elds of degree 12 with class number one there are exactly nine such cm elds

a controllability condensed form and a state feedback pole assignment algorithm for descriptor systems a direct algorithm for the pole assignment problem of a time invariant linear multivariable descriptor system with linear state feedback is presented the system is assumed to be completely controllable for both finite and infinite poles the algorithm is based on the controllability condensed form which is derived

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems