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1
Content available Global stability of positive discrete-time time-varying nonlinear feedback systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
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2021
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Vol. 3, No. 1
17--20
EN
The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
2
Content available Influence of chloride ion corrosion on the performance of reinforced concrete beam bridge in offshore environment
Gao Y. H.
Archives of Civil Engineering
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2020
|
Vol. 66, nr 2
253--265
EN
Chloride ion erosion in offshore environment may damage the mechanical properties of beam bridges. In this study, the reinforced concrete specimen was designed, accelerated erosion experiments were carried out to simulate the coastal corrosion environment, and the corrosion rate, nominal strength and equivalent strength of steel bars, concrete cracks and reliability of beam bridges were calculated to understand the time-varying mechanical properties of beam bridges. The results showed that the nominal and equivalent strength of reinforcing bars decreased with the increase of corrosion rate of reinforcing bars. The change of yield strength was greater than that of equivalent strength. The change of crack width of concrete showed a slow-fast-slow trend, and the reliability of beam bridges decreased significantly in about 50 years. The experimental results show that chloride ion corrosion can significantly damage the mechanical properties of the beam bridge and affect the time-varying reliability of the beam bridge. Therefore, it is necessary to carry out timely maintenance and inspection and take effective methods to control steel corrosion to ensure the safety of the use of the beam bridge.
3
Content available remote A class of positive and stable time-varying electrical circuits
Kaczorek T.
Przegląd Elektrotechniczny
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2015
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R. 91, nr 5
121-124
EN
The positivity and stability of a class of time-varying continuous-time linear systems and electrical circuits are addressed. Sufficient conditions for the positivity and asymptotic stability of the systems are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.
PL
W pracy rozpatrywana jest dodatniość I stabilność asymptotyczna pewnej klasy obwodów elektrycznych o zmiennych w czasie parametrach. Podano warunki dostateczne dodatniości i stabilności asymptotycznej układów i obwodów elektrycznych. Pokazano, że istnieje obszerna klasa dodatnich i stabilnych asymptotycznie obwodów elektrycznych o zmiennych w czasie parametrach. Rozważania zilustrowano przykładami obwodów elektrycznych.
4
Content available Positive and stable time-varying continous-time linear systems and electrical circuits
Kaczorek T.
Poznan University of Technology Academic Journals. Electrical Engineering
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2015
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No. 81
11--19
EN
The positivity and stability of a class of time-varying continuous-time linear systems and electrical circuits are addressed. Sufficient conditions for the positivity and asymptotic stability of the system are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.
5
Content available Positivity and stability of time-varying fractional discrete-time linear systems
Kaczorek T., Borawski K.
Measurement Automation Monitoring
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2015
|
Vol. 61, No. 3
84--87
EN
Necessary and sufficient conditions for the positivity of time-varying fractional discrete-time linear systems are established. The problem of asymptotic stability of the positive time-varying fractional discrete-time linear systems is analyzed and sufficient conditions are given. Considerations are illustrated by numerical examples.
6
Content available A computer algorithm for the solution of the Astate equation for time-varying fractional discrete-time linear systems
Kaczorek T., Borawski K.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 1
2--4
EN
Method for finding of the solution of the state equation for time-varying fractional discrete-time linear systems is proposed and computer algorithm is presented. The effectiveness of the proposed algorithm is demonstrated on numerical examples.
7
Positivity and stability of time-varying linear electrical circuits
Kaczorek T.
Logistyka
|
2015
|
nr 3
2060--2071, CD 1
EN
The positivity and asymptotic stability of time-varying linear electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the time-varying linear systems and electrical circuits are established. Using the Lyapunov method the asymptotic stability of a large class of positive electrical circuits is shown. Examples of positive and asymptotically stable electrical circuits are presented.
PL
Praca poświęcona jest badaniu dodatniości i stabilności asymptotycznej liniowych układów i obwodów elektrycznych o zmiennych w czasie parametrach. Podano warunki konieczne i wystarczające dodatniości liniowych układów i obwodów elektrycznych zmiennych w czasie parametrach. Pokazano, że istnieje obszerna klasa liniowych obwodów elektrycznych dodatnich o zmiennych w czasie parametrach. Podano również warunki dostateczne oraz proste kryteria badania stabilności tej klasy liniowych układów i obwodów elektrycznych. Rozważania zilustrowano przykładami dodatnich stabilnych asymptotycznie liniowych obwodów elektrycznych o zmiennych w czasie parametrach.
8
Content available Analysis of positivity and stability of time-varying continuous-time linear systems and electrical circuits
Kaczorek T.
Computer Applications in Electrical Engineering
|
2015
|
Vol. 13
1--18
EN
The positivity and stability of a class of time-varying continuous-time linear systems and electrical circuits are addressed. Sufficient conditions for the positivity and asymptotic stability of the system are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. The Lyapunov method is extended to positive nonlinear systems. Examples of positive electrical circuits are presented.
9
Content available Model of time-varying linear systems and Kolmogorov equations
Krumov A. V.
Archives of Control Sciences
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2015
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Vol. 25, no. 2
201--214
EN
In the paper an approximate model of time-varying linear systems using a sequence of timeinvariant systems is suggested. The conditions for validity of the approximation are proven with a theorem. Examples comparing the numerical solution of the original system and the analytical solution of the model are given. For the system under the consideration a new criterion giving sufficient conditions for robust Lagrange stability is suggested. The criterion is proven with a theorem. Examples are given showing stable and non stable solutions of a time-varying system and the results are compared with the numerical Runge-Kutta solution of the system. In the paper an important application of the described method of solution of linear systems with timevarying coefficients, namely analytical solution of the Kolmogorov equations is shown.
10
Content available remote RSA Problem for Varying Traffic in Flexible Optical Networks
Olszewski I
Image Processing & Communications
|
2014
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Vol. 19, no. 1
35--44
EN
The problem of service time-varying traffic in flexible transparent optical networks, assuming that the incoming connections and their duration are not known in advance, is considered in this work. Time-varying traffic requires dynamic spectrum allocation for connections implemented in the network. In the considered problem, a path with the required spectrum around the reference frequency is determined for each incoming connection by the routing algorithm. In order to take into account the dynamic spectrum allocation for the connections in the network, two spectrum expansion/- contraction schemes have been applied on the basis of which the average blocking probability for the incoming request additional slot was determined.
11
Content available remote Locally Positive Nonlinear Systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 4
505-509
EN
The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.
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