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1
Content available Zeroing the transfer matrix of the Roesser model of 2-D linear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
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2023
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Vol. 33, no. 4
513--519
EN
Controllability, observability and the transfer matrix of the discrete 2-D Roesser model are analyzed. It is shown that the controllability of the Roesser model is invariant under state feedbacks and the observability under output feedbacks. Sufficient conditions are established for the zeroing of the transfer matrix of the Roesser model.
2
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.
3
Content available Holdability and stabilizability of 2D Roesser model
Kaczorek T.
Control and Cybernetics
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2003
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Vol. 32, no 1
75-86
EN
The holdability and stabilizability problem of 2D Roesser model is formulated and solved. Conditions for the existence of solution to the problem are established. Two procedures for computation of a gain matrix of the state-feedback are proposed and illustrated by a numerical example.
PL
Sformułowano i rozwiązano zadanie utrzymywania i stabilizowalności dla dwuwymiarowego modelu Roessera. Ustalono warunki istnienia rozwiązania tego zadania. Zaproponowano dwie procedury wyliczania macierzy przejścia w pętli sprzężenia zwrotnego względem stanu i zilustrowano je przykładem numerycznym.
4
Content available remote Elimination of Finite Eigenvalues of the 2d Roesser Model by State Feedbacks
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2001
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Vol. 11, no 2
369-376
EN
A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.
5
Content available remote Extensions of the Gersgorin's Theorem for Regular Pencils and Stable 2D Roesser Models
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1999
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Vol. 47, nr 1
75-81
EN
The classical Gersgorin's theorem is extended for regular pencils and stable Roesser models. The extension for regular pencils is based on application of the elementary row and column operations to polynominal matrix of the regular pencil. The extended Gersgorin's theorem for regular pencils is illustrated by an example.
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