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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 remote New stability conditions for positive continuous-discrete 2D linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 3
521-524
EN
New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.
3
Content available remote Similarity transformation of matrices to one common canonical form and its applications to 2D linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 3
507-512
EN
The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one, (ii) the reduced 2D system is positive if and only if the linear transformation matrix is monomial. Necessary and sufficient conditions are established for the existence of a gain matrix such that the matrices of the closed-loop system can be reduced to the common canonical form.
4
Content available remote Asymptotic stability of positive fractional 2D linear systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2009
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Vol. 57, nr 3
289-292
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