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1
Content available Analysis of the descriptor Roesser model with the use of the Drazin inverse
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2015
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Vol. 25, no. 3
539--546
EN
A method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example.
2
Content available Komputerowe metody badania stabilności modelu Roessera liniowych układów 2D
Busłowicz M., Rzepecki A. E.
Pomiary Automatyka Robotyka
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2012
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R. 16, nr 2
298-302
PL
Rozpatrzono problem badania asymptotycznej stabilności liniowych układów dynamicznych dwuwymiarowych (2D). Podano komputerowe metody badania asymptotycznej stabilności modelu Roessera w przypadku ogólnym oraz analityczną metodę w przypadku szczególnym układu skalarnego. Rozważania zilustrowano przykładami liczbowymi.
EN
The problem of asymptotic stability of linear dynamic 2D systems is considered. Computer methods for asymptotic stability analysis of the Roesser model in the general case and analytic method in the case of scalar systems are given. The considerations are illustrated by numerical examples.
3
Content available General Response Formula for Fractional 2D Continuous-Time Linear Systems Described by the Roesser Model
Rogowski K.
Acta Mechanica et Automatica
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2011
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Vol. 5, no. 2
112-116
EN
A new class of fractional two-dimensional (2D) continuous-time linear systems is introduced. The general response formula for the system is derived using a 2D Laplace transform. It is shown that the classical Cayley-Hamilton theo- rem is valid for such class of systems. Usefulness of the general response formula to obtain a solution of the system is discussed and illustrated by a numerical example.
4
Content available remote Positivity and stabilization of fractional 2D linear systems described by the Roesser model
Kaczorek T., Rogowski K.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 1
85-92
EN
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.
5
Content available remote The choice of the forms of Lyapunov functions for a positive 2D Roesser model
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 4
471-475
EN
The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix ATPA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.
6
Content available remote Determination of reachability subspace of two-dimensional positive linear systems described by Roesser model
Markowski K.A.
Przegląd Elektrotechniczny
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2005
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R. 81, nr 3
89-92
EN
A method of determinination reachability subspace of the positive two dimension systems described by Roesser model using digraph theory is proposed. A procedure for computation of the reachability subspace is also proposed. The procedure illustrated by a numerical example.
PL
Przedstawiono metodę wyznaczania obszaru osiągalności dodatnich układów dwuwymiarowych opisanych za pomocą modelu Roessera. Zaproponowaną procedurę zilustrowano prostym przykładem numerycznym.
7
Content available remote Controllability and reconstructability of a system described by the N-D Roesser model
Kurek J. E.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 1
55-60
EN
The controllability and reconstructability (global) of the system described by a digital N-D Roesser model are defined. Then, necessary and sufficient conditions for system controllability and reconstructability are given. The conditions constitute a generalization of the corresponding conditions for 1-D systems.
8
Content available remote Canonical Forms of Singular 1 D and 2 D Linear Systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 1
61-72
EN
The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence of a pair of nonsingular block diagonal matrices transforming the matrices of the singular 2D Roesser model to their canonical forms are established. A procedure for computing the pair of nonsingular matrices is presented.
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