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    Wyświetlanie 1-15 z 15
    Tytuł:
    Bilateral Polynomial Equations With Unimodular Right-Hand-Side Matrices
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/908092.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    automatyka
    robotyka
    bilateral
    polynomial equation
    unimodular procedure
    solution
    Opis:
    Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 511-514
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the computation of the minimal polynomial of a polynomial matrix
    Autorzy:
    Karampetakis, P.
    Tzekis, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/908531.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    wielomian minimalny
    dyskretna transformacja Fouriera
    macierz wielomianowa
    macierzowe równanie liniowe
    minimal polynomial
    discrete Fourier transform
    polynomial matrix
    linear matrix equations
    Opis:
    The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 3; 339-349
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Relationship Between the Infinite Eigenvalue Assignment for Singular Systems and the Solvability of Polynomial Matrix Equations
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/908199.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    automatyka
    robotyka
    assignment
    infinite eigenvalue
    singular
    polynomial matrix equation
    system
    reliationship
    Opis:
    Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 161-167
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Computation of the Set of Positive Solutions to Polynomial Matrix Equations
    Autorzy:
    Kaczorek, T.
    Łopatka, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/911183.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    obliczanie
    równanie macierzowe
    computation
    set of positive solutions
    polynomial matrix equation
    Opis:
    Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method of computing of the set of positive solutions to a polynomial diophatine equation based on extreme points and extreme directions is proposed. The effectiveness of the method is demonstrated on a numerical example.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2000, 10, 2; 309-320
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and determination of the set of Metzler matrices for given stable polynomials
    Autorzy:
    Kaczorek, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/331407.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    oznaczanie
    istnienie
    macierz Metzlera
    wielomian
    stabilność
    determination
    existence
    Metzler matrix
    polynomial
    stability
    Opis:
    The problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 389-399
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polynomial systems theory applied to the analysis and design of multidimensional systems
    Autorzy:
    Hatonen, J.
    Ylinen, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/908252.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    informatyka
    nD systems
    module of fractions
    partial differential equations
    polynomial systems theory
    Opis:
    The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting on X can be extended to its field of fractions F(p). The conditions on the pair (F[p],X) are quite restrictive, i.e. each non-zero a(p)\in F[p] has to be an automorphism on X before the extension is possible. However, when this condition is met, say for operators { p1,p2,..., pn-1}, a polynomial ring F[p1,p2,...,pn] acting on X can be extended to F(p1,p2,..., pn-1)[pn], resulting in a principal ideal domain structure. Hence in this case all the rigorous principles of `ordinary' polynomial systems theory for the analysis and design of systems is applicable. As an example, both an observer for estimating non-measurable outputs and a stabilizing controller for a distributed parameter system are designed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 1; 15-27
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Proper feedback compensators for a strictly proper plant by polynomial equations
    Autorzy:
    Callier, F. M.
    Kraffer, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/908450.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    liniowy układ stacjonarny
    sprzężenie zwrotne
    macierz wielomianowa
    równanie wielomianowe
    linear time-invariant feedback control systems
    polynomial matrix systems
    row-column-reduced polynomial matrices
    feedback compensator design
    flexible belt device
    Opis:
    We review the polynomial matrix compensator equation XlDr + YlNr = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (Nr,Dr) is given by the strictly proper rational plant right matrix-fraction P = NrD-1 r , (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (Xl, Yl) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction C = X-1 l Yl. We recall first the class of all polynomial matrix pairs (Xl, Yl) solving (COMP) and then single out those pairs which result in a proper rational compensator. An important role is hereby played by the assumptions that (a) the plant denominator Dr is column-reduced, and (b) the closed-loop characteristic matrix Dk is row-column-reduced, e.g., monically diagonally degree-dominant. This allows us to get all solution pairs (Xl, Yl) giving a proper compensator with a row-reduced denominator Xl having (sufficiently large) row degrees prescribed a priori. Two examples enhance the tutorial value of the paper, revealing also a novel computational method.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 4; 493-507
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation
    Autorzy:
    Costa, R.
    Machado, G. J.
    Clain, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/330268.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    finite volume method
    polynomial reconstruction operator
    harmonic operator
    biharmonic operator
    high order method
    Opis:
    A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one-dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 3; 529-537
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two-stage instrumental variables identification of polynomial Wiener systems with invertible nonlinearities
    Autorzy:
    Janczak, Andrzej
    Korbicz, Józef
    Powiązania:
    https://bibliotekanauki.pl/articles/330751.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    nonlinear system
    parameter estimation
    dynamic model
    polynomial model
    układ nieliniowy
    estymacja parametru
    model dynamiczny
    model wielomianowy
    Opis:
    A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 3; 571-580
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems
    Autorzy:
    Vardulakis, A. I. G.
    Karampetakis, N. P.
    Antoniou, E. N.
    Tictopoulou, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/907853.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    macierz wielomianowa
    nierozkładalność
    przestrzeń stanu
    polynomial matrices
    realization theory
    minimality
    irreducibility
    generalized state space
    infinite decoupling zeros
    Opis:
    We review the realization theory of polynomial (transfer function) matrices via 'pure' generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is defined and the mechanism of the 'cancellations' of 'decoupling zeros at infinity' is closely examined. The difference between the concepts of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts of dynamic and non-dynamic variables appearing in generalized state space realizations are also examined.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 1; 77-88
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the computation of the GCD of 2-D polynomials
    Autorzy:
    Tzekis, P.
    Karampetakis, N. P.
    Terzidis, H. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/929803.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    największy wspólny dzielnik
    dyskretne przekształcenie Fouriera
    wielomian dwuzmienny
    greatest common divisor
    discrete Fourier transform
    two-variable polynomial
    Opis:
    The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 463-470
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A study on new right/left inverses of nonsquare polynomial matrices
    Autorzy:
    Hunek, W. P.
    Latawiec, K. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907786.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ wielowymiarowy
    macierz wielomianowa
    sterowanie minimalnowariancyjne
    multivariable systems
    right/left inverses of polynomial matrices
    Smith factorization
    minimum variance control
    Opis:
    This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called [...]-inverses, [...]-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The application-oriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 2; 331-348
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On hyper-regularity and unimodularity of Ore polynomial matrices
    Autorzy:
    Fritzsche, K.
    Röbenack, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/331500.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Ore polynomial matrice
    hyper regularity
    unimodularity
    meromorphic function
    differential operator
    noncommutativity
    hyper regular inverse
    macierz wielomianowa
    macierz unimodularna
    funkcja meromorficzna
    operator różniczkowy
    Opis:
    We investigate Ore polynomial matrices, i. e., matrices with polynomial entries in d/dt whose coefficients are meromorphic functions in t and as such constitute a non-commutative ring. In particular, we study the properties of hyper-regularity and unimodularity of such matrices and derive conditions which make it possible to efficiently check for these characteristics. In addition, this approach enables computation of hyper-regular left and right and unimodular inverses.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 3; 583-594
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equivalence and reduction of delay-differential systems
    Autorzy:
    Boudellioua, M. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/911236.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    opis macierzowy
    układ z opóźnieniem
    równoważność systemu
    bazy Gröbnera
    polynomial matrix description
    neutral delay-differential systems
    strict system equivalence
    determinantal ideals
    Gröbner bases
    Opis:
    A new direct method is presented which reduces a given high-order representation of a control system with delays to a firstorder form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann’s strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 1; 15-22
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
    Autorzy:
    Tagade, P. M.
    Choi, H. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/330516.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Bayesian framework
    stochastic partial differential equation
    Karhunen–Loève expansion
    generalized polynomial chaos
    dynamically biorthogonal field equations
    ramy Bayesa
    stochastyczne równanie różniczkowe
    przekształcenie Karhunena-Loeve'a
    chaos wielomianowy
    Opis:
    This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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