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1
Content available Global stability of discrete-time feedback nonlinear systems with descriptor positive linear parts and interval state matrices
Kaczorek Tadeusz, Ruszewski Andrzej
International Journal of Applied Mathematics and Computer Science
|
2022
|
Vol. 32, no. 1
5--10
EN
The global stability of discrete-time nonlinear systems with descriptor positive linear parts, positive scalar feedbacks and interval state matrices is addressed. Sufficient conditions for the global stability of this class of nonlinear systems are established. The effectiveness of these conditions is illustrated using numerical examples.
2
Content available Global stability of nonlinear feedback systems with fractional positive linear parts
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2020
|
Vol. 30, no. 3
493--499
EN
The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).
3
Content available Absolute stability of a class of fractional positive nonlinear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 1
93--98
EN
The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.
4
Content available remote Normal positive linear systems and electrical circuits
Kaczorek T.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 6
1--7
EN
The notion of normal positive electrical circuits is introduced and some their specific properties are investigated. New state matrices of positive linear systems and electrical circuits are proposed and their properties are analyzed. It is shown that positive electrical circuits with diagonal state matrices are normal for all values of resistances, inductances and capacitances.
PL
W artykule zaproponowano pojęcie dodatniego obwodu elektrycznego oraz przeanalizowano specjalne własności dodatnich układów i obwodów elektrycznych. Wykazano, że dodatnie obwody elektryczne z diagonalnymi macierzami stanu są zawsze normalne dla wszystkich wartości rezystancji, indukcyjności i pojemności.
5
Content available Stability of interval positive fractional discrete-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 3
451--456
EN
The aim of this work is to show that interval positive fractional discrete-time linear systems are asymptotically stable if and only if the respective lower and upper bound systems are asymptotically stable. The classical Kharitonov theorem is extended to interval positive fractional linear systems.
6
Content available Robust controlled positive delayed systems with interval parameter uncertainties: A delay uniform decomposition approach
Elloumi W., Mehdi D., Chaabane M.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 3
441--450
EN
This paper is concerned with robust stabilization of continuous linear positive time-delay systems with parametric uncertainties. The delay considered in this work is a bounded time-varying function. Previously, we have demonstrated that the equidistant delay-decomposition technique is less conservative when it is applied to linear positive time-delay systems. Thus, we use simply a delay bi-decomposition in an appropriate Lyapunov–Krasovskii functional. By using classical and partitioned control gains, the state-feedback controllers developed in our work are formulated in terms of linear matrix inequalities. The efficiency of the proposed robust control laws is illustrated with via an example.
7
Content available Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure
Markowski K. A.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 1
9--24
EN
In the last two decades, fractional calculus has become a subject of great interest in various areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned by Leibniz and L'Hospital. Fractional calculus has been found to be a very useful tool for modeling linear systems. In this paper, a method for computation of a set of a minimal positive realization of a given transfer function of linear fractional continuous-time descriptor systems has been presented. The proposed method is based on digraph theory. Also, two cases of a possible input-output digraph structure are investigated and discussed. It should be noted that a digraph mask is introduced and used for the first time to solve a minimal positive realization problem. For the presented method, an algorithm was also constructed. The proposed solution allows minimal digraph construction for any one-dimensional fractional positive system. The proposed method is discussed and illustrated in detail with some numerical examples.
8
Content available Decentralized stabilization of fractional positive descriptor continuous-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 1
135--140
EN
A method for decentralized stabilization of fractional positive descriptor linear systems is proposed. Necessary and sufficient conditions for decentralized stabilization of fractional positive descriptor linear systems are established. The efficiency of the proposed method is demonstrated on a numerical example.
9
Content available Positivity and stability of fractional descriptor time-varying discrete-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
|
Vol. 26, no. 1
5--13
EN
The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor time-varying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
10
Content available Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2015
|
Vol. 25, no. 4
827--831
EN
The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.
11
Content available Positivity of a class of fractional descriptor continuous-time nonlinear systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2015
|
Vol. 63, nr 2
561--565
EN
The positivity of a class of fractional descriptor continuous-time nonlinear systems is addressed by the use of the Weierstrass- Kronecker decomposition of the pencil of linear part of nonlinear system. Sufficient conditions for the positivity are established and illustrated by an example of fractional continuous-time descriptor nonlinear systems.
12
Content available Minimum energy control of fractional positive continuous-time linear systems with bounded inputs
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
Vol. 24, no. 2
335--340
EN
A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
13
Content available Minimum energy control of fractional descriptor positive discrete-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
Vol. 24, no. 4
735--743
EN
Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.
14
Content available Approximation of positive stable continuous-time linear systems by positive stable discrete-time systems
Kaczorek T.
Pomiary Automatyka Robotyka
|
2013
|
R. 17, nr 2
359-364
EN
The positive asymptotically stable continuous-time linear systems are approximated by positive asymptotically stable discretetime linear systems by the use of Pade type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. The stabilization problem of positive unstable continuous-time and corresponding discrete-time linear systems by state-feedbacks is also addressed.
PL
Dodatnie układy stabilne ciągłe są aproksymowane za pomocą liniowej aproksymacji Pade dodatnimi, stabilnymi układami dyskretnymi. Wykazano, że aproksymacja ta zachowuje dodatniość i stabilność asymptotyczną. Rozważania ogólne zostały zilustrowane przykładem numerycznym.
15
Content available remote Wyznaczanie macierzy stanu dodatniego układu 2D na podstawie wielomianu charakterystycznego
Markowski K.
Przegląd Elektrotechniczny
|
2007
|
R. 83, nr 2
109-112
PL
W artykule przedstawiono metodę wyznaczanie elementów macierzy stanu dodatniego układu dwuwymiarowego (2D) opisanego za pomocą modelu ogólnego używając teorii dwuwymiarowych grafów skierowanych oddziaływań. Metodę zilustrowano przykładem numerycznym.
EN
In this paper a method for determination elements of the state matrices of two-dimensional (2D) systems described by general model using digraphs theory is presented. The method is illustrated by numerical examples.
16
Content available Componentwise asymptotic stability and exponential stability of positive discrete-time linear systems with delays
Busłowicz M., Kaczorek T.
Pomiary Automatyka Kontrola
|
2006
|
R. 52, nr 7/8
31-33
EN
Definitions of the componentwise asymptotic stability and of the exponential stability are extended for positive discrete-time linear systems with delays. Necessary and sufficient conditions for the componentwise asymptotic stability and the exponential stability are established.
PL
Definicje asymptotycznej stabilności według składowych oraz stabilności wykładniczej rozszerzono na liniowe dodatnie układy dyskretne z opóźnieniami. Podano warunki konieczne i 90 starczające asympto-tycznej stabilności według składowych oraz stabilności wykładniczej.
17
Istnienie i wyznaczanie realizacji dodatnich układów z opóźnieniami
Kaczorek T.
Pomiary Automatyka Kontrola
|
2005
|
R. 51, nr 9 bis
7--15
PL
Przedstawiono syntetycznie aktualny stan badań dotyczących wyznaczania dodatnich realizacji minimalnych układów dyskretnych i ciągłych z opóźnieniami. Poza znanymi, wcześniej publikowanymi, praca zawiera nowe wyniki niepublikowane oraz niektóre aktualne problemy otwarte w obszarze dodatnich liniowych układów z opóźnieniami.
EN
An overview of slate ol art of the existence and computation of minimal realizations of positive discrete-time and continuous-time systems with delays is presented. Sufficient conditions for the existence of minimal realizations for given proper rational transfer functions are established. Procedures for computations of minimal realizations are presented. The procedures are illustrated hy numerical examples.
18
Content available Osiągalność i obserwowalność układów dodatnich ze sprzężeniami zwrotnymi
Kaczorek T.
Pomiary Automatyka Kontrola
|
2000
|
R. 46, nr 7
2-5
PL
W pracy wykazano, że: 1. osiągalność i obserwowalność układów dodatnich nie sa niezmiennicze względem sprzężenia zwrotnego, 2. dla ukladu dodatniego nieosiągalnego i nieobserwowalnego w n-krokach można dobrać macierz sprzężenia zwrotnego tak, aby uklad ze sprzężeniem zwrotnym był układem dodatnim osiagalnym i sterowalnym w n-krokach. Podano warunki konieczne i wystarczające na to, aby uklad dodatni był jednoczesnie osiągalny i obserwowalny.
EN
It is shown that: 1. the reachability and observability of positive linear systems are invariant under the state-feedbacks, 2. it is possible closed loop system is reachable and observable. Necessary and sufficient conditions are established for the simultaneous reachability of positive linear discrete-time systems.
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