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1
Content available Invariance of reachability and observability for fractional positive linear electrical circuit with delays
Yuan Tong, Yang Hongli
Archives of Electrical Engineering
|
2021
|
Vol. 70, nr 3
513--530
EN
This paper focuses on the invariance of the reachability and observability for fractional order positive linear electrical circuits with delays and their checking methods. By derivation and comparison, it shows that conditions and checking methods of reachability and observability for integer and fractional order positive linear electrical circuits with delays are invariant. An illustrative example is presented at the end of the paper.
2
Content available Minimum energy control of 2D positive continuous-discrete linear systems
Kaczorek T.
Acta Mechanica et Automatica
|
2014
|
Vol. 8, no. 3
165--168
EN
The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.
3
Content available remote Constructability and observability of standard and positive electrical circuits
Kaczorek T.
Przegląd Elektrotechniczny
|
2013
|
R. 89, nr 7
132--136
EN
The constructability and observability of standard and positive electrical circuits composed of resistors, coils, condensators and voltage (current) sources are addressed. Necessary and sufficient conditions for the constructability and observability of the positive electrical circuits are established. Effectiveness of the conditions is demonstrated on examples of positive electrical circuits.
PL
W pracy rozpatruje się standardowe i dodatnie obwody elektryczne złożone z rezystorów, cewek i kondensatorów oraz źródeł napięcia i prądu. Podano warunki konieczne i wystarczające odtwarzalności i obserwowalności tych obwodów elektrycznych. Warunki te zostały zlustrowane na przykładach dodatnich obwodów elektrycznych.
4
Content available Reachability and controllability of positive fractional-order discrete-time systems
Trzasko W.
Pomiary Automatyka Robotyka
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2013
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R. 17, nr 2
365-370
EN
In the paper the positive linear discrete-time noncommensurate fractional-order systems described by the state equations are considered. Definition and necessary and sufficient conditions for the positivity, reachability and controllability to zero are given and proven. The considerations are illustrated by a numerical example.
PL
W pracy rozpatrzono liniowe stacjonarne dodatnie układy dyskretne niecałkowitego niewspółmiernego rzędu. Sformułowano definicje oraz podano warunki konieczne i wystarczające dodatniości, osiągalności i sterowalności układów dyskretnych niewspółmiernego rzeczywistego rzędu oraz współmiernego niecałkowitego rzędu. Rozważania zilustrowano przykładem numerycznym.
5
Content available Positive electrical circuits and their reachability
Kaczorek T.
Archives of Electrical Engineering
|
2011
|
Vol. 60, nr 3
283-301
EN
Conditions for the positivity of linear electrical circuits composed of resistances, coils, capacitors and voltage (current) sources are established. It is shown that: 1) the electrical circuit composed of resistors, coils and voltage source is positive for any values of their resistances, inductances and source voltages if and only if the number of coils is less or equal to the number of its linearly independent meshes, 2) the electrical circuit is not positive for any values of its resistances, capacitances and source voltages if each its branch contains resistor, capacitor and voltage source, 3) the positive n-meshes electrical circuit with only one inductance in each linearly independent mesh is reachable if all resistances of branches belonging to two linearly independent meshes are zero.
6
Content available Positivity and Reachability of Fractional Electrical Circuits
Kaczorek T.
Acta Mechanica et Automatica
|
2011
|
Vol. 5, no. 2
42-51
EN
Conditions for the positivity of fractional linear electrical circuits composed of resistors, coils, condensators and voltage (current) sources are established. It is shown that: 1) the fractional electrical circuit composed of resistors, coils and voltage source is positive for any values of their resistances, inductances and source voltages if and only if the number of coils is less or equal to the number of its linearly independent meshes, 2) the fractional electrical circuit is not positive for any values of its resistances, capacitances and source voltages if each its branch contains resistor, capacitor and voltage source, It is also shown that the fractional positive electrical circuits of R, C, e type are reachable if and only if the conductances between their nodes are zero and the fractional positive electrical circuits of R, L, e type are reachable if and only if the resistances belonging to two meshes are zero.
7
Content available Inverse systems of linear systems
Kaczorek T.
Archives of Electrical Engineering
|
2010
|
Vol. 59, nr 3-4
203-216
EN
The concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable. 2) The inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. 3) The inverse system of continuous-time and discrete-time linear systems are reachable if and only if the standard systems are reachable. The considerations are illustrated by numerical examples.
8
Content available remote Reachability of cone fractional continuous-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 1
89-93
EN
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
9
Content available remote Positive 2D discrete-time linear Lyapunov systems
Przyborowski P., Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 1
95-105
EN
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
10
Content available remote Fractional positive continuous-time linear systems and their reachability
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2008
|
Vol. 18, no 2
223-228
EN
A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
11
Content available remote Controllability and observability of linear discrete-time fractional-order systems
Guermah S., Djennoune S., Bettayeb M.
International Journal of Applied Mathematics and Computer Science
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2008
|
Vol. 18, no 2
213-222
EN
In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
12
Content available Reachability and minimum energy control of positive discrete-time linear systems with multiple delays in state and control
Kaczorek T., Busłowicz M.
Pomiary Automatyka Kontrola
|
2007
|
R. 53, nr 10
40-44
EN
A notion of positive linear discrete-time systems with multiple delays in state and control is introduced. The necessary and sufficient conditions for positivity, reachability and minimum energy control are given. Considerations are illustrated by example.
PL
W pracy podano warunki, przy spełnieniu których liniowy dyskretny układ z wieloma opóźnieniami zmiennych stanu i sterowania jest układem dodatnim. Podano też warunki konieczne i wystarczające osiągalności oraz sterowania z minimalną energią. Rozważania zilustrowano przykładem.
13
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.
14
Content available remote Monomial Subdigraphs of Reachable and Controllable Positive Discrete-time Systems
Bru R., Cacetta L., Rumchev V. G.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 1
159-166
EN
A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix A may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents. The criteria identify not only the reachability and controllability properties of positive linear systems, but also their reachable and controllable parts (subsystems) when the system does not possess such properties.
15
Content available remote Reachability and minimum energy control of positive 2D systems with delays
Kaczorek T.
Control and Cybernetics
|
2005
|
Vol. 34, no 2
411-423
EN
The notion of internally positive 2D model (system) with delays is introduced. Solution of the 2D linear models with delays is derived. Necessary and sufficient conditions for the internal positivity and reachability of the models are established. The Cayley-Hamilton theorem for the 2D linear models with delays is extended. The minimum energy control for the internally positive 2D models with delays is formulated and solved.
16
Content available remote Towards a solution to a plan-formation problem
Winkowski J.
Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk
|
2002
|
Nr 948
1-18
EN
The paper deals with the problem of achieving a goal in a system in which certain actions can be executed. The initial state and the states that may be reached from this state by executing actions are represented by sets of sente nces, each sentence saying that some objects are or are not in a relation. Available actions are represented as instances of rewriting rules. The problem consists in finding a sequence of actions that leads from the initia l state to a state in which the goal is achieved. The presented solution to this problem for a class of systems is based on reducing it to the problem of reachability in contextual Petri nets.
PL
Praca dotyczy problemu osiągania celu w systemie, w którym można wykonywać pewne akcje. Stan początkowy i stany, które moga być z tego stanu osiągnięte przez wykohnywanire akcji, są reprezentowane przez zbiory zadań, z których każde orzeka, że pewne obiekty są lub nie są w pewnych relacjach. Możliwe akcje sa reprezentowane jako instancje pewnych reguł przekształcania. Problem polega na znalezieniu ciągu akcji prowadzącego ze stanu początkowego do stanu, w którym cel jest osiągnięty. Proponowane rozwiązanie tego problemu dla pewnej klasy systemów polega na jego redukowaniu do problemu osiągalności w kontekstowych sieciach Petriego.
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