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1
Content available Singular Fractional Continuous-Time and Discrete-Time Linear Systems
Kaczorek T.
Acta Mechanica et Automatica
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2013
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Vol. 7, no. 1
26-33
EN
New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and 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 systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.
2
Content available Kryteria obserwowalności układów dyskretnych singularnych niecałkowitego rzędu
Kociszewski R.
Pomiary Automatyka Robotyka
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2012
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R. 16, nr 2
328-331
PL
W pracy rozpatrzono zagadnienie obserwowalności dyskretnych układów singularnych, opisanych w przestrzeni stanu równaniem rzędu niecałkowitego. Pokazano, że przy pewnych warunkach oceny obserwowalności tego układu można dokonać, stosując kryteria znane dla standardowych układów rzędu całkowitego. Rozważania teoretyczne zilustrowano przykładem liczbowym.
EN
The paper presents a problem of observability of discrete- time singular fractional systems. It has been shown that after decomposition of considered system into two independent systems: regular (standard) fractional system and singular system (with a nilpotent matrix N) observability conditions can be formulated in reference to standard fractional discrete-time system. Proposed approach is possible to use if the matrix N = 0. The considerations are illustrated by a numerical example.
3
Singular fractional linear systems and electrical circuits
Kaczorek T.
Logistyka
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2011
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nr 3
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 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 with only ideal supercondensators and voltage sources or at least one node with branches with supercoils.
PL
Zaproponowano metodę analizy singularnych układów liniowych niecałkowitego rzędu, która może być stosowana na przykład do obwodów elektrycznych. Korzystając z definicji Caputo róźniczko-całki niecałkowitego rzędu, dekompozycji Weierstrassa pęku regularnego oraz transformaty Laplacea podano rozwiązanie równania stanu singularnych liniowych układów niecałkowitego rzędu. Wykazano że każdy obwód elektryczny jest singularnycm układem niecałkowitego rzędu jeśli zawiera przynajmniej jedno oczko składające się z gałęzi zawierających idealne superkondensatory i źródła napięcia lub przynajmniej jeden węzeł do którego dochodzą gałęzie zawierające supercewki.
4
Content available remote Singular fractional linear systems and electrical circuits
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
|
Vol. 21, no 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.
5
Content available Singular fractional discrete-time linear systems
Kaczorek T.
Control and Cybernetics
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2011
|
Vol. 40, no 3
753-761
EN
A new class of singular fractional linear discretetime systems is introduced. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional linear systems is derived. The considerations are illustrated by numerical examples.
6
Computation of positive realizations of singular hybrid linear systems - two cases
Sajewski Ł.
Systems Science
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2009
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Vol. 35, no 2
27-39
EN
The realization problem for 2D positive linear hybrid systems is addressed. Two methods based on the state variable diagram for finding positive realizations of a given improper transfer function are proposed. Sufficient conditions for the existence of a positive realization of a given improper transfer function are established. Procedures for computation of a positive realization are proposed and illustrated by numerical examples.
7
Content available Computation of positive realizations of SISO singular hybrid linear systems
Kaczorek T., Sajewski Ł.
Journal of Automation Mobile Robotics and Intelligent Systems
|
2009
|
Vol. 3, No. 2
8-13
EN
The realization problem for 2D positive singular linear hybrid systems is formulated, as well as a method based on the state variable diagram for finding a positive realization of a given improper transfer function is proposed. Sufficient conditions for the existence of a positive realization of a given improper transfer function are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.
8
Content available Symulacja singularnych liniowych układów ciągłych
Rogowski K., Kaczorek T.
Pomiary Automatyka Kontrola
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2008
|
R. 54, nr 9
620-622
PL
Podano nową metodę symulacji singularnych liniowych układów ciągłych opartą na dekompozycji Weierstrassa-Kroneckera na trzy podukłady: standardowy, ściśle singularny i statyczny. Metoda została zilustrowana przykładem numerycznym i przebiegami czasowymi.
EN
A new metod of singular continous-time linear systems simulation based on Weierstrass-Kronecker decomposition for three: standard, strictly singular and static subsystems is presented. Illustrating numerical example with simulations results are given.
9
Content available remote Realization problem for singular positive continuous-time systems with delays
Kaczorek T.
Control and Cybernetics
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2007
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Vol. 36, no 1
47-57
EN
The positive realization problem for a class of singular continuous-time linear SISO systems with delays in state and in output is addressed. The notions of canonical forms of matrices and of dual systems are extended for singular linear systems with delays. Necessary and sufficient conditions for positivity of SISO singular continuous-time systems with delays and sufficient conditions for the existence of a positive singular realization are established. A procedure for computation of a positive singular realization of a given transfer function is proposed and illustrated by a numerical example.
10
Solutions of nonlinear singular boundary value problems
Sebai H.
Journal of Applied Analysis
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2005
|
Vol. 11, nr 1
95-112
EN
We suty the existence of solutions to a class of problems u" + f(t,u)=0, u(0)=u(1)=0 where f(t, .) is allowed to be singular at t=0, t=1.
11
A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian
Jiang D. Q., O'Regan D., Agarwal R. P.
Journal of Applied Analysis
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2005
|
Vol. 11, nr 1
35-47
EN
This paper presents new existence results for singular discrete boundary value problems for the one-dimension p-Laplacian. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign. Our results are new even for p = 2
12
Content available remote Shifting to infinity of the eigenvalues in singular linear systems
Kaczorek T.
Przegląd Elektrotechniczny
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2003
|
R. 79, nr 6
439-443
PL
Sformułowano warunki konieczne i wystarczające przesuwania do nieskończoności wartości własnych za pomocą sprzężeń zwrotnych w singularnych układach liniowych. Podano dwie procedury wyznaczania macierzy sprzężeń zwrotnych, które przesuwają do nieskończoności wartości własne układów zamkniętych. Procedury te zilustrowano przykładami liczbowymi.
EN
Necessary and sufficient conditions for the shifting to infinity of the eigenvalues by state-feedbacks in singular linear systems are established. Two procedures for computing of the state-feedback gain matrix are proposed and illustrated by numerical examples.
13
Content available remote The Relationship Between the Infinite Eigenvalue Assignment for Singular Systems and the Solvability of Polynomial Matrix Equations
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2003
|
Vol. 13, no 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.
14
Content available remote Canonical Forms of Singular 1 D and 2 D Linear Systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2003
|
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.
15
Content available remote Singular Compartmental Linear Systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2003
|
Vol. 51, nr 4
409-419
EN
Models of singular compartmental linear continuous-time and discrete-time systems are introduced. Solutions of the singular models in terms of the Drazin inverse of the models matrices are given. Necessary and sufficient conditions for the singular systems to be compartmental are established. A notion of P-equivalence is introduced and conditions for the P-equivalence of the compartmental and asymptotically stable positive system are derived.
16
Content available remote A Novel Approach to Design of Minimal Order Functional Observers for Singular Linear Systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2003
|
Vol. 51, nr 2
181-188
EN
A novel approach to design of minimal order functional observers for singular linear systems is proposed. A procedure for computation of matrices of the minimal order functional observers is presented and illustrated by numerical example.
17
Content available remote Externally and internally positive singular discrete-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2002
|
Vol. 12, no 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.
18
Content available remote Solutions of Standard Models Equivalent to Singular 2D Models
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2000
|
Vol. 48, nr 1
93-104
EN
A new extended Roesser type model is introduced and its solution is derived. Sufficient conditions are established under which a singular 2D general model can be reduced to standard 2D general models. Solution to the new model is also derived.
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