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Number of results: 6
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Abstract

In this note, a formula for the lower Bohl exponent of a discrete system with variable coefficients and weak variation was proved. This formula expresses the Bohl exponent through the eigenvalues of the coefficient matrix. Based on these formulas a necessary and sufficient condition for an uniform exponential instability of such systems is also presented.
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Authors and Affiliations

Adam Czornik
1
Krzysztof Simek
1

  1. Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, Akademicka Street 16, 44-101 Gliwice, Poland
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Abstract

The dynamic development of science requires constant improvement of approaches to modeling physical processes and phenomena. Practically all scientific problems can be described by systems of differential equations. Many scientific problems are described by systems of differential equations of a special class, which belong to the group of so-called singularly perturbed differential equations. Mathematical models of processes described by such differential equations contain a small parameter near the highest derivatives, and it was the presence of this small factor that led to the creation of a large mathematical theory. The work proposes a developed algorithm for constructing uniform asymptotics of solutions to systems of singularly perturbed differential equations.
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Authors and Affiliations

Valentyn Sobchuk
1
ORCID: ORCID
Iryna Zelenska
1
ORCID: ORCID
Oleksandr Laptiev
1
ORCID: ORCID

  1. Taras Shevchenko National University of Kyiv, Ukraine
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Abstract

Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.
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Authors and Affiliations

Adam Czornik
1
Evgenii Makarov
2
Michał Niezabitowski
3
Svetlana Popova
4
Vasilii Zaitsev
4

  1. Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, 44-100 Gliwice, Poland
  2. Institute of Mathematics, National Academy of Sciencesof Belarus, 220072 Minsk, Belarus
  3. Faculty of Automatic Control, Electronics and Computer Science,Silesian University of Technology, 44-100 Gliwice, Poland
  4. Udmurt State University, 426034 Izhevsk, Russia
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Abstract

Consider the semilinear system defined by

x(i+1) = Ax(i) + f(x(i)), i≥ 0

x(0) = x0 ϵ ℜn

and the corresponding output signal y(i)=Cx(i), i ≥ 0, where A is a n x n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω in ℜp if the output signal (y(i))i associated to our system satisfies the condition y(i) in Ω, for every integer i ≥ 0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems (controlled and uncontrolled systems). Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.

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Authors and Affiliations

Amine El Bhih
Youssef Benfatah
ORCID: ORCID
Mostafa Rachik
ORCID: ORCID
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Abstract

This paper addresses the problem of designing secure control for networked multi-agent systems (MASs) under Denial-of-Service (DoS) attacks. We propose a constructive design method based on the interaction topology. The MAS with a non-attack communication topology, modelled by quasi-Abelian Cayley graphs subject to DoS attacks, can be represented as a switched system. Using switching theory, we provide easily implementable sufficient conditions for the networked MAS to remain asymptotically stable despite DoS attacks. Our results are applicable to both continuous-time and discrete-time systems, as well as to discrete-time systems with variable steps or systems that combine discrete and continuous times.
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Authors and Affiliations

Ewa Girejko
1
ORCID: ORCID
Agnieszka B. Malinowska
1
ORCID: ORCID

  1. Bialystok University of Technology,Wiejska 45, 15-351 Białystok, Poland
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Abstract

Child-authored poetry is one of the most remarkable and fascinating phenomena in the contemporary Chinese poetry world. However, for all its immense popularity among Chinese readers and attractivity for professional, adult poets, due to its unclear ontological status and lack of well-proven methodological tools that would be easily applicable to it, it has thus far remained beyond the scope of literary-critical and scholarly interests. The present paper offers a broad panoramic view of Chinese children’s poetry through six case studies of individual young authors and collective initiatives aimed at the artistic activization of certain groups of children, discussing the educational and social significance of children’s poetry writing, its complicated reception patterns, as well as its entanglement with various literary-political discourses. Subsequently, the study delves into the aesthetic, conceptual, and philosophical aspects of children’s works. The final part analyses the essential theoretical-philosophical questions that child-authored verse asks with regard to poetry at large, prompting us to rethink notions such as authorship or “poeticness” and the definition of poetry per se. The author proposes the metaphor of asymptotic freedom to illustrate how marginal phenomena of questionable status contribute to maintaining the distinctness and coherence of the field of poetry as a whole.
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Authors and Affiliations

Joanna Krenz
1

  1. Adam Mickiewicz University, Poznań, Poland

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