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1
Content available Perfect observer resistant to the changes of dynamics of the standard linear system
Sławiński M. A.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2017
|
Vol. 65, nr 3
313--316
EN
The article presents a class of perfect observers for standard continuous-time linear systems. Observers are resistant to significant changes in the dynamics of the system. The value of poles of the system can be unlimited as long as their number does not change and the conditions presented in this article are satisfied. There are presented numerical examples and simulations results.
2
Content available remote Oustaloup parallel approximation
Bauer W., Baranowski J., Dziwiński T., Piątek P., Zagórowska M.
Prace Naukowe Politechniki Śląskiej. Elektryka
|
2016
|
z. 3-4
59--64
EN
This article presents Oustaloup approximation method for fractional differential systems, which has been modified by the authors. Application of this method by using numerical experiments has been shown and behavior of discrete system has been analyzed.
PL
W artykule przedstawiono zmodyfikowaną przez autorów metodę aproksymacji Oustaloupa dla układów różniczkowych niecałkowitego rzędu. Pokazano jej wykorzystanie poprzez eksperyment numeryczny oraz przeanalizowano zachowanie systemu dyskretnego.
3
Content available Stability conditions for linear continuous-time fractional-order state-delayed systems
Busłowicz M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 1
3--7
EN
The stability problem of continuous-time linear fractional order systems with state delay is considered. New simple necessary and sufficient conditions for the asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix and time delay. It is shown that in the complex plane there exists such a region that location in this region of all eigenvalues of the state matrix multiplied by delay in power equal to the fractional order is necessary and sufficient for the asymptotic stability. Parametric description of boundary of this region is derived and simple new analytic necessary and sufficient conditions for the stability are given. Moreover, it is shown that the stability of the fractional order system without delay is necessary for the stability of this system with delay. The considerations are illustrated by a numerical example.
4
Content available Descriptor fractional discrete-time linear system with two different fractional orders and its solution
Sajewski Ł.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 1
15--20
EN
Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.
5
Content available The selected problems of controllability of discrete-time switched linear systems with constrained switching rule
Babiarz A., Czornik A., Klamka J., Niezabitowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2015
|
Vol. 63, nr 3
657--666
EN
In this paper the controllability problem for discrete-time linear switched systems is considered. The main goal is to find a control signal that steers any initial state to a given final state independently of the switching signal. In the paper, it is assumed that there are some constraints posed on the switching signal. Moreover, we present a necessary and sufficient conditions of some kinds of controllability. Three types of controllability, namely: from zero initial state to any final state, from any initial state to zero final state and from any initial state to any final state are considered. Finally, three illustrative examples are shown.
6
Content available Positive Realizations for Descriptor Discrete-Time Linear Systems
Kaczorek T.
Acta Mechanica et Automatica
|
2012
|
Vol. 6, no. 2
58-61
EN
Conditions for the existence of positive realizations for descriptor discrete-time linear systems are established. A procedure for computation of positive realizations for improper transfer matrices is proposed. The effectiveness of the method is demonstrated on numerical example.
7
Content available General Response Formula for Fractional 2D Continuous-Time Linear Systems Described by the Roesser Model
Rogowski K.
Acta Mechanica et Automatica
|
2011
|
Vol. 5, no. 2
112-116
EN
A new class of fractional two-dimensional (2D) continuous-time linear systems is introduced. The general response formula for the system is derived using a 2D Laplace transform. It is shown that the classical Cayley-Hamilton theo- rem is valid for such class of systems. Usefulness of the general response formula to obtain a solution of the system is discussed and illustrated by a numerical example.
8
Content available Solvability of 2D hybrid linear systems - comparsion of three different methods
Kaczorek T., Marchenko V., Sajewski Ł.
Acta Mechanica et Automatica
|
2008
|
Vol. 2, no. 2
59-66
EN
A class of positive hybrid linear systems is introduced. Three different methods for computation of solutions of the hybrid system are proposed. The considerations are illustrated by numerical example. Simulations of solution have been shown for the methods.
9
Content available Realization problem for singular positive single-input single-output continuous-time systems with delays in state and in inputs
Kaczorek T.
Acta Mechanica et Automatica
|
2008
|
Vol. 2, no. 2
45-50
EN
The positive realization problem for singular continuous-time linear single-input single-output systems with delays in state and in inputs is addressed. The notion of canonical forms of matrices are extended for singular linear systems with delays. Necessary and sufficient conditions for positivity of the 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
Content available Positive different orders fractional 2D linear systems
Kaczorek T.
Acta Mechanica et Automatica
|
2008
|
Vol. 2, no. 2
51-58
EN
A new class of positive different orders fractional 2D linear systems is introduced. A notion of (á, â) orders difference of 2D function is proposed. Fractional 2D state equations of linear systems are given and their solutions are derived using 2D Z-transform. The classical Cayley-Hamilton theorem is extended to the 2D fractional linear systems. Neccesary and sufficient conditions for the positivity, reachability and controllability to zero of the fractional 2D linear systems are established.
11
A short survey of recent representation results for linear system maps
Sandberg I. W.
Zeszyty Naukowe. Telekomunikacja i Elektronika / Akademia Techniczno-Rolnicza w Bydgoszczy
|
2006
|
z. 9
9-24
EN
We give an expression for the most general input-output map assiociated with the members of a certain important of multidimensional linear shift-invariant systems with bounded Lebesgue-measurable inputs. The expression given is an iterated function-space limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution with an integrable impulse-response function. A key role is played by a certain family of weighting operators. It is observed that for the large family of inputs and maps addressed, the Dirac impulse-response concept is in fact not the key concept concerning the representation of H, and that instead the input-output properties of H arc determined in general by a certain type of family of responses. Some related material concerning other results, engineering education, and discrete-space systems, is also given.
PL
W artykule zostało przedstawione ogólne wyrażenie opisujące odwzorowanie zbioru sygnałów wejściowych na zbiór sygnałów wyjściowych, związane z elementami pewnej bardzo ważnej, dużej rodziny wielowymiarowych, liniowych oraz stacjonar-nych systemów określonych dla sygnałów wejściowych ograniczonych i mierzalnych w sensie Lebesgue'a. Wyrażenie to stanowi granicę splotu zdefiniowanego w iterowa-nej przestrzeni funkcyjnej. W pracy został również podany warunek konieczny i do-stateczny, pod którym ww. granica może być przedstawiona jako splot z odpowiedzią impulsową w postaci funkcji całkowalnej. Kluczową rolę pełni w tym przypadku pewna rodzina operatorów wagowych. Pokazano też, że dla dużej rodziny przyjętych zbiorów sygnałów wejściowych i odwzorowań, koncepcja odpowiedzi impulsowej otrzymywanej w wyniku pobudzenia systemu tzw. impulsem Diraca nie jest kluczowa dla opisu systemu H. To znaczy, że zamiast tej koncepcji właściwości systemu H w konwencji wejścia-wyjścia mogą być, w ogólności, określone za pomocą pewnej rodziny odpowiedzi. W artykule przedstawiono również inne pokrewne wyniki, doty-czące systemów dyskretnych oraz aspektów edukacyjnych.
12
Content available remote Modelowanie liniowych systemów stacjonarnych za pomocą systemów Laguerre'a
Ciesielski G.
Kwartalnik Elektroniki i Telekomunikacji
|
2000
|
Vol. 46, nr 2
129-147
PL
Artykuł omawia zagadnienia identyfikacji strukturalnej i parametrycznej modeli liniowych systemów stacjonarnych. Do opisu przyjęto strukturę modeli Laguerre'a. Przedstawiona tu teoria wynika z jednolitej ogólnej teorii operatorowej systemów, zarówno liniowych jak i nieliniowych. Jednolita ogólna teoria operatorowa systemów jest rozwijana przez autorów artykułu od szeregu lat ([7] - [24]). W artykule omówiono również program Turbo Wiener TM, opracowany i rozwijany przez autora dla systemu operacyjnego MS Windows, który pozwala wyznaczyć modele i korektory systemów stacjonarnych, zarówno liniowych jak i nieliniowych, wykorzystując przy tym wspomnianą jednolitą ogólną teorię operatorową systemów. Przedstawiono tu również wyniki obliczeń otrzymanych za pomocą programu Turbo Wiener TM, dla typowych liniowych systemów stacjonarnych.
EN
The problem of structure and parameter identifications of models of linear time - invariant system is presented in this paper. The structure of Laguerre models is applied to they describes. Presented theory invoves from uniform general operator's theory of systems linear as well as nonlinear. Uniform general operator's theory of systems has evaluated by author of this paper, from several years ([7] - [24]). In this paper, the Turbo Wiener TM program, designed and evaluated by authors for MS Windows operational system, is presented. This program lets to calculate the models and correctors of time - invariant systems which are linear nonlinear. There is applied uniform general operator's theory of systems. This paper presents too the results of computation by use of program Turbo Wiener TM for typical linear time - invariant systems.
13
Content available remote Korekcja liniowych systemów stacjonarnych za pomocą systemów Laguerre'a
Ciesielski G.
Kwartalnik Elektroniki i Telekomunikacji
|
2000
|
Vol. 46, nr 2
149-161
PL
Artykuł omawia zagadnienia identyfikacji strukturalnej i parametrycznej modeli korektorów liniowych systemów stacjonarnych. Do ich opisu przyjęto strukturę modeli Laguerre'a. Przedstawiona tu teoria wynika z jednolitej ogólnej teorii operatorowej systemów, zarówno liniowych jak i nieliniowych. Jednolita ogólna teoria operatorowa systemów jest rozwijana przez autora artykułu od szeregu lat ([7] - [24]). W artykule omówiono również program Turbo Wiener TM, opracowany i rozwijany przez autora dla systemu operacyjnego MS Windows, który pozwala wyznaczyć modele i korektory systemów stacjonarnych, zarówno liniowych jak i nieliniowych, wykorzystując przy tym wspomnianą jednolitą ogólną teorię operatorową systemów. Przedstawiono tu również wyniki obliczeń otrzymanych za pomocą programu Turbo Wiener TM, dla korektorów typowych liniowych systemów stacjonarnych.
EN
The problem of structure and parameter identifications of correctors models of linear time-invariant system is presented in this paper. The structure of Laguerre models is applied to they describes. Presented theory involes from uniform general operator's theory of systems linear as well as nonlinear. Uniform general operator's theory of systems has evaluated by author of this paper, from several years ([7] - [24]). In this paper, the Turbo Wiener TM program, designed and evaluated by autors for MS Windows operational system, is presented. This program lets to calculated the models and correctors of time - invariant systems, which are linear or nonlinear. There is applied uniform general operator's general theory of systems. This paper presents too the results of computation by use of program Turbo Wirner TM for correctors of typical linear time - invariant systems.
14
Content available Frequency responses of linear interval plants with delay
Busłowicz M.
Control and Cybernetics
|
1999
|
Vol. 28, no 2
281-289
EN
The paper gives a simple new method for computing envelopes of the magnitude and phase plots of the family of linear time-invariant interval plants with uncertain delay. The undelayed part of the plant is described by the family of interval transfer functions (the nominator and denominator polynomials are interval polynomials). The proposed method requires the knowledge of the Kharitonov polynomials associated with the nominator and denominator polynomials.
15
Content available remote Prefactorization methods for some subclasses of H-matrices
Cvetkovic L., Nedic J.
Demonstratio Mathematica
|
1998
|
Vol. 31, nr 4
789-800
EN
The development of the prefactorization methods introduced by Woźnicki started in 1968. Since then, these methods have been successfully applied to solving large systems of linear equations, arising from finite difference approximation applied to the second order elliptic equations. Prefactorization methods also proved to be a very efficient tool for solving linear systems with strictly diagonally dominant matrices. For increasing the rate of convergence single or double successive overrelaxation processes can be used. Determining the convergence area for relaxation parameters seems to be still an interesting problem. In this paper we present the convergence analysis for some prefactorization methods in a case when matrix belongs to some subclasses of H-matrices which are generalizations of strictly diagonally dominant matrices.
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