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Abstract

In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.

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Authors and Affiliations

Muhafzan
Admi Nazra
Lyra Yulianti
Zulakmal
Refi Revina
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Abstract

The paper is a newapproach to the Duhamel integral. It contains an overviewof formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
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Authors and Affiliations

Michał Różański
1
Beata Sikora
1
ORCID: ORCID
Adrian Smuda
1
Roman Wituła
1

  1. Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

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