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1
Content available remote Controllability and reconstructability of a system described by the N-D Roesser model
100%
Kurek J. E.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
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nr 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.
2
Content available Pontryagin’s maximum principle for the Roesser model with a fractional Caputo derivative
100%
Yusubov S. S. , Mahmudov E. N.
Archives of Control Sciences
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2024
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tom Vol. 34, No. 2
271--300
EN
In this paper, we study the modern mathematical theory of the optimal control problem associated with the fractional Roesser model and described by Caputo partial derivatives, where the functional is given by the Riemann-Liouville fractional integral. In the formulated problem, a new version of the increment method is applied, which uses the concept of an adjoint integral equation. Using the Banach fixed point principle, we prove the existence and uniqueness of a solution to the adjoint problem. Then the necessary and sufficient optimality condition is derived in the form of the Pontryagin’s maximum principle. Finally, the result obtained is illustrated by a concrete example.
3
Content available Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model
88%
Rogowski K.
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2011
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tom Vol. 59, nr 2
195-200
EN
A new class of fractional 2D Lyapunov systems described by the Roesser models is introduced. Necessary and sufficient conditions for the positivity and asymptotic stability of the new class of systems are established. It is shown that the checking of the asymptotic stability of positive 2D fractional Lyapunov systems can be reduced to testing the asymptotic stability of corresponding positive standard 1D discretetime systems. The considerations are illustrated by a numerical example.
4
Content available remote Positivity and stabilization of fractional 2D linear systems described by the Roesser model
88%
Kaczorek T. , Rogowski K.
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tom 20
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nr 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 Analysis of the descriptor Roesser model with the use of the Drazin inverse
88%
Kaczorek T.
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tom 25
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nr 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.
6
Content available remote Equivalence of nD Singular Roesser and Fornasini-Marchesini Models
88%
Kaczorek T.
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1999
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tom Vol. 47, nr 3
235-246
EN
A new nD Roesser model with extended inputs is introduced. nD Roesser models with square matrices and extended inputs equivalent to the singular nD Fornasini-Marchesini models and nD Fornasini-Marchesini models with square matrices equivalent to the singular nD Roesser models are derived. A formula determination the solution of standard 2D Roesser model with extended inputs is also derived.
7
Content available General Response Formula for Fractional 2D Continuous-Time Linear Systems Described by the Roesser Model
75%
Rogowski K.
Acta Mechanica et Automatica
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2011
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tom 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.
8
Content available Komputerowe metody badania stabilności modelu Roessera liniowych układów 2D
75%
Busłowicz M. , Rzepecki A. E.
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2012
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tom 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.
9
Content available remote Positivity and stabilization of fractional 2D linear systems described by the Roesser model
63%
Kaczorek T. , Rogowski K.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 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.
10
Content available remote Determination of reachability subspace of two-dimensional positive linear systems described by Roesser model
63%
Markowski K. A.
Przegląd Elektrotechniczny
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2005
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tom 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.
11
Content available On the solution of the implicit Roesser model
51%
Karampetakis N. P.
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