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Canonical forms of singular 1D and 2D linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 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.
2
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Singular fractional linear systems and electrical circuits

86%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 2
379-384
EN
A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.
3
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The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations

86%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 2
161-167
EN
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.
4
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Externally and internally positive singular discrete-time linear systems

86%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 2
197-202
EN
Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it is not internally positive.
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