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Wyświetlanie 1-15 z 17
Tytuł:
Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model
Autorzy:
Ruszewski, A.
Powiązania:
https://bibliotekanauki.pl/articles/229234.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
asymptotic stability
practical stability
fractional order
discrete-time linear system
Opis:
The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.
Źródło:
Archives of Control Sciences; 2016, 26, 4; 441-452
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Eigenvalue assignment in fractional descriptor discrete-time linear systems
Autorzy:
Kaczorek, T.
Borawski, K.
Powiązania:
https://bibliotekanauki.pl/articles/229985.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
eigenvalue assignment
fractional
descriptor
discrete time linear system
gain matrix
Opis:
The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.
Źródło:
Archives of Control Sciences; 2017, 27, 1; 119-128
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis and comparison of the stability of discrete-time and continuous-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/229420.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
analysis
comparison
stability
discrete-time
continuous-time
linear system
Opis:
The asymptotic stability of discrete-time and continuous-time linear systems described by the equations xi+1 = Ākxi and x(t) = Akx(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix Āk and of the continuous-time systems depends only on phases of the eigenvalues of the matrix Ak, 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.
Źródło:
Archives of Control Sciences; 2016, 26, 4; 551-563
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Relationship between the observability of standard and fractional linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/230092.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional
standard
linear
discrete-time
continuous-time
system
observability
Opis:
The relationship between the observability of standard and fractional discrete-time and continuous-time linear systems are addressed. It is shown that the fractional discrete-time and continuous-time linear systems are observable if and only if the standard discrete-time and continuous-time linear systems are observable.
Źródło:
Archives of Control Sciences; 2017, 27, 3; 441-451
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive stable realizations of discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/201627.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
positive
stable
realization
existence
procedure
linear
discrete-time
system
Opis:
The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 3; 605-616
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems
Autorzy:
Busłowicz, M.
Ruszewski, A.
Powiązania:
https://bibliotekanauki.pl/articles/201743.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
linear system
discrete-time
fractional
practical stability
asymptotic stability
Opis:
In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 4; 779-786
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Simple analytic conditions for stability of fractional discrete-time linear systems with diagonal state matrix
Autorzy:
Busłowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/201685.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
linear system
discrete-time
fractional
practical stability
asymptotic stability
Opis:
In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems with a diagonal state matrix are addressed. Standard and positive systems are considered. Simple necessary and sufficient analytic conditions for practical stability and for asymptotic stability are established. The considerations are illustrated by numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 4; 809-814
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Computation of initial conditions and inputs for given outputs of fractional and positive discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/229803.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
computation
initial condition
observability
positive
discrete-time
linear
system
Opis:
The problem of computation of initial conditions and inputs for given outputs of fractional standard and positive discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for existence of solution to the problem are established. It is shown that there exist the unique solutions to the problem only if the pair (A, C) of the system is observable.
Źródło:
Archives of Control Sciences; 2012, 22, 2; 145-159
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition
Autorzy:
Kaczorek, T.
Borawski, K.
Powiązania:
https://bibliotekanauki.pl/articles/229539.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
descriptor
discrete-time
linear
system
Weierstrass-Kronecker decomposition
minimum energy control
Opis:
The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.
Źródło:
Archives of Control Sciences; 2016, 26, 2; 177-187
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/949806.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
discrete-time
linear
positive
system
monomial Frobenius generalized matrix
reachability
observability
Opis:
The notions of monomial generalized Frobenius matrices is proposed and the reachability and observability of positive discrete-time linear systems with positive and negative integer powers of the state matrices is addressed. Necessary and sufficient conditions for the reachability of the positive systems are established.
Źródło:
Archives of Control Sciences; 2018, 28, 1; 119-133
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An extension of Klamka’s method to positive descriptor discrete-time linear systems with bounded inputs
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/229979.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
descriptor
positive
discrete-time
linear
system
Weierstrass-Kronecker decomposition
minimum energy control
Opis:
The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.
Źródło:
Archives of Control Sciences; 2018, 28, 2; 255-268
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Responses of positive standard and fractional linear systems and electrical circuits with derivatives of their inputs
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/201416.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
positive fractional linear system
continuous-time
discrete-time
response formula
dyskretny czas
układ ułamkowy
ciągłość czasowa
Opis:
Responses of positive standard and fractional continuous-time and discrete-time linear systems with derivatives of their inputs are presented herein. It is shown that the formulae for state vectors and outputs are also valid for their derivatives if the inputs and outputs and their derivatives of suitable order are zero for t = 0. Similar results are also shown for positive standard and fractional discrete-time linear systems.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 419-425
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Drazin inverse matrix method for fractional descriptor discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/201040.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Drazin inverse
descriptor
fractional
discrete-time
linear system solution
odwrotność Drazina
deskryptor
układy dyskretne
system liniowy
Opis:
The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditions for a given set of admissible inputs is established. The proposed method is illustrated by a numerical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 395-399
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new approach to the realization problem for fractional discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/200792.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional system
linear system
discrete-time system
computation procedure
realization
transfer matrix
macierz transferu
system liniowy
procedura obliczeniowa
sterowanie
Opis:
A new approach to the realization problem for fractional discrete-time linear systems is proposed. A procedure for computation of fractional realizations of given transfer matrices is presented and illustrated by numerical examples.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 1; 9-14
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed terminal time fractional optimal control problem for discrete time singular system
Autorzy:
Chiranjeevi, Tirumalasetty
Devarapalli, Ramesh
Babu, Naladi Ram
Vakkapatla, Kiran Babu
Rao, R. Gowri Sankara
Garcìa Màrquez, Fausto Pedro
Powiązania:
https://bibliotekanauki.pl/articles/2175112.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional order differential equation
discrete time singular system
fractional derivative
linear quadratic optimal control problem
Opis:
This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
Źródło:
Archives of Control Sciences; 2022, 32, 3; 489--506
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 17

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