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Abstract

The main focus of the paper is on the asymptotic behaviour of linear discrete-time positive systems. Emphasis is on highlighting the relationship between asymptotic stability and the structure of the system, and to expose the relationship between null-controllability and asymptotic stability. Results are presented for both time-invariant and time-variant systems.

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Authors and Affiliations

G. James
V. Rumchev
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Abstract

In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
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Bibliography

[1] A. Abdelhakim and J. Tenreiro Machado: A critical analysis of the conformable derivative, Nonlinear Dynamics, 95 (2019), 3063–3073, DOI: 10.1007/s11071-018-04741-5.
[2] K. Balachandran, Y. Zhou and J. Kokila: Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 3508–3520, DOI: 10.1016/j.cnsns.2011.12.018.
[3] K. Balachandran, J. Kokila, and J.J. Trujillo: Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Apllications, 64 (2012), 3037–3045, DOI: 10.1016/j.camwa.2012.01.071.
[4] P. Duch: Optimization of numerical algorithms using differential equations of integer and incomplete orders, Doctoral dissertation, Lodz University of Technology, 2014 (in Polish).
[5] C. Guiver, D. Hodgson and S. Townley: Positive state controllability of positive linear systems. Systems and Control Letters, 65 (2014), 23–29, DOI: 10.1016/j.sysconle.2013.12.002.
[6] R.E. Gutierrez, J.M. Rosario and J.T. Machado: Fractional order calculus: Basic concepts and engineering applications, Mathematical Problems in Engineering, 2010 Article ID 375858, DOI: 10.1155/2010/375858.
[7] T. Kaczorek: Positive 1D and 2D Systems, Communications and Control Engineering, Springer, London 2002.
[8] T. Kaczorek: Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science, 18 (2008), 223–228, DOI: 10.2478/v10006-008-0020-0.
[9] T. Kaczorek: Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences, 58 (2010), 453–458, DOI: 10.2478/v10175-010-0043-1.
[10] T. Kaczorek: Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Science, 411, 2011.
[11] T. Kaczorek: Constructability and observability of standard and positive electrical circuits, Electrical Review, 89 (2013), 132–136.
[12] T. Kaczorek: An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Sciences: Technical Sciences, 62 (2014), 227–231, DOI: 10.2478/bpasts-2014-0022.
[13] T. Kaczorek: Minimum energy control of fractional positive continuoustime linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science, 24 (2014), 335–340, DOI: 10.2478/amcs-2014-0025.
[14] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits, Springer, Studies in Systems, Decision and Control, 13 2015.
[15] T. Kaczorek: A class of positive and stable time-varying electrical circuits, Electrical Review, 91 (2015), 121–124. DOI: 10.15199/48.2015.05.29.
[16] T. Kaczorek: Computation of transition matrices of positive linear electrical circuits, BUSES – Technology, Operation, Transport Systems, 24 (2019), 179–184, DOI: 10.24136/atest.2019.147.
[17] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, 2006.
[18] J. Klamka: Controllability of Dynamical Systems, Kluwer Academic Publishers, 1991.
[19] T.J.Machado,V. Kiryakova and F. Mainardi: Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation, 6 (2011), 1140–1153, DOI: 10.1016/j.cnsns.2010.05.027.
[20] K.S. Miller and B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Calculus, Villey, 1993.
[21] A. Monje, Y. Chen, B.M. Viagre, D. Xue and V. Feliu: Fractional-order Systems and Controls. Fundamentals and Applications, Springer-Verlag, 2010.
[22] K. Nishimoto: Fractional Calculus: Integrations and Differentiations of Arbitrary Order, University of New Haven Press, 1989.
[23] K.B. Oldham and J. Spanier: The Fractional Calculus, Academic Press, 1974.
[24] I. Podlubny: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, In: Mathematics in Science and Engineering, Academic Press, 1999.
[25] S.G. Samko, A.A. Kilbas and O.I. Marichev: Fractional Integrals and Derivatives: Theory and Applications, Gordan and Breach Science Publishers, 1993.
[26] J. Sabatier, O.P. Agrawal and J.A. Tenreiro Machado: Advances in Fractional Calculus, In: Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, 2007.
[27] B. Sikora: Controllability of time-delay fractional systems with and without constraints, IET Control Theory & Applications, 10 (2016), 1–8, DOI: 10.1049/iet-cta.2015.0935.
[28] B. Sikora: Controllability criteria for time-delay fractional systems with a retarded state, International Journal of Applied Mathematics and Computer Science, 26 (2016), 521–531, DOI: 10.1515/amcs-2016-0036.
[29] B. Sikora and J. Klamka: Constrained controllability of fractional linear systems with delays in control, Systems and Control Letters, 106 (2017), 9–15, DOI: 10.1016/j.sysconle.2017.04.013.
[30] B. Sikora and J. Klamka: Cone-type constrained relative controllability of semilinear fractional systems with delays, Kybernetika, 53 (2017), 370–381, DOI: 10.14736/kyb-2017-2-0370.
[31] B. Sikora: On application of Rothe’s fixed point theorem to study the controllability of fractional semilinear systems with delays, Kybernetika, 55 (2019), 675–689, DOI: 10.14736/kyb-2019-4-0675.
[32] T. Schanbacher: Aspects of positivity in control theory, SIAM J. Control and Optimization, 27 (1989), 457–475.
[33] B. Trzasko: Reachability and controllability of positive fractional discretetime systems with delay, Journal of Automation Mobile Robotics and Intelligent Systems, 2 (2008), 43–47.
[34] J. Wei: The controllability of fractional control systems with control delay, Computers and Mathematics with Applications, 64 (2012), 3153–3159, DOI: 10.1016/j.camwa.2012.02.065.
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Authors and Affiliations

Beata Sikora
1
ORCID: ORCID
Nikola Matlok
1

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

In high technologies today, wearable devices have become popular. Wearable technology is a body sensing system that supports application of health observance and tracking through a wearable Global Positioning System (GPS). The design of the patch antennas is highly significant for the brilliance of the wearable patch antennas. This paper focuses on analyzing the bending effect on return loss and frequency between three types of GPS patch antenna. Types of GPS patch antennas that have been designed in this project are with different substrates and different designs. The wearable patch antenna has been designed and analyse using CST software. As a result, able to analysis the reflection coefficient (S11), radiation patterns, and analytical approach for patch antenna bending effect were obtained.
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Authors and Affiliations

Kavinesh S Radhakrishna
1
M.S. Shakhirul
1
Y.S. Lee
1 2
K.N. Khairina
1
A.R.A Syafiqah
1

  1. Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis (UniMAP), Perlis, Malaysia
  2. Advanced Communication Engineering, Centre of Excellence (CoE), Universiti Malaysia Perlis (UniMAP), Perlis, Malaysia
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Abstract

Presently, digitalization is causing continuous transformation of industrial processes. However, it does pose challenges like spatially contextualizing data from industrial processes. There are various methods for calculating and delivering real-time location data. Indoor positioning systems (IPS) are one such method, used to locate objects and people within buildings. They have the potential to improve digital industrial processes, but they are currently underutilized. In addition, augmented reality (AR) is a critical technology in today’s digital industrial transformation. This article aims to investigate the use of IPS and AR in manufacturing, the methodologies and technologies employed, the issues and limitations encountered, and identify future research opportunities. This study concludes that, while there have been many studies on IPS and navigation AR, there has been a dearth of research efforts in combining the two. Furthermore, because controlled environments may not expose users to the practical issues they may face, more research in a real-world manufacturing environment is required to produce more reliable and sustainable results.
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Authors and Affiliations

Kuhelee Chandel
1
Julia Åhlén
1
Stefan Seipel
1 2

  1. Department of Computer and Geospatial Sciences, University of Gävle, Sweden
  2. Division of Visual Information and Interaction, Department of Information Technology, Uppsala University, Sweden
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Abstract

The paper proposes a new, state space, finite dimensional, fractional order model of a heat transfer in one dimensional body. The time derivative is described by Caputo operator. The second order central difference describes the derivative along the length. The analytical formulae of the model responses are proved. The stability, convergence, and positivity of the model are also discussed. Theoretical results are verified by experiments.
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Bibliography

[1] R. Almeida and D.F.M. Torres: Necessary and sufficient conditions for the fractional calculus of variations with caputo derivatives. Communications in Nonlinear Science and Numerical Simulation, 16(3), (2011), 1490–1500, DOI: 10.1016/j.cnsns.2010.07.016.
[2] A. Atangana and D. Baleanu: New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer. Thermal Sciences, 20(2), (2016), 763–769, DOI: 10.2298/TSCI160111018A.
[3] R. Caponetto, G. Dongola, L. Fortuna, and I. Petras: Fractional order systems: Modeling and Control Applications. In: Leon O. Chua, editor, World Scientific Series on Nonlinear Science, pages 1–178. University of California, Berkeley, 2010.
[4] S. Das: Functional Fractional Calculus for System Identyfication and Control. Springer, Berlin, 2010.
[5] M. Dlugosz and P. Skruch: The application of fractional-order models for thermal process modelling inside buildings. Journal of Building Physics, 39(5), (2016), 440–451, DOI: 10.1177/1744259115591251.
[6] A. Dzielinski, D. Sierociuk, and G. Sarwas: Some applications of fractional order calculus. Bulletin of the Polish Academy of Sciences, Technical Sciences, 58(4), (2010), 583–592, DOI: 10.2478/v10175-010-0059-6.
[7] C.G. Gal and M. Warma Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory, 5(1), (2016), 61–103, DOI: 10.3934/eect.2016.5.61.
[8] T. Kaczorek Fractional positive contiuous-time linear systems and their reachability. International Journal of Applied Mathematics and Computer Science, 18(2), (2008), 223–228, DOI: 10.2478/v10006-008-0020-0.
[9] T. Kaczorek: Singular fractional linear systems and electrical circuits. International Journal of Applied Mathematics and Computer Science, 21(2), (2011), 379–384, DOI: 10.2478/v10006-011-0028-8.
[10] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology, Bialystok, 2014.
[11] A. Kochubei: Fractional-parabolic systems, preprint, arxiv:1009.4996 [math.ap], 2011.
[12] W. Mitkowski: Approximation of fractional diffusion-wave equation. Acta Mechanica et Automatica, 5(2), (2011), 65–68.
[13] W. Mitkowski: Finite-dimensional approximations of distributed rc networks. Bulletin of the Polish Academy of Sciences. Technical Sciences, 62(2), (2014), 263–269, DOI: 10.2478/bpasts-2014-0026.
[14] W. Mitkowski,W. Bauer, and M. Zagorowska: Rc-ladder networks with supercapacitors. Archives of Electrical Engineering, 67(2), (2018), 377– 389, DOI: 10.24425/119647.
[15] K. Oprzedkiewicz: The discrete-continuous model of heat plant. Automatyka, 2(1), (1998), 35–45 (in Polish).
[16] K. Oprzedkiewicz: The interval parabolic system. Archives of Control Sciences, 13(4), (2003), 415–430.
[17] K. Oprzedkiewicz:Acontrollability problem for a class of uncertain parameters linear dynamic systems. Archives of Control Sciences, 14(1), (2004), 85–100.
[18] K. Oprzedkiewicz: An observability problem for a class of uncertainparameter linear dynamic systems. International Journal of Applied Mathematics and Computer Science, 15(3), (2005), 331–338.
[19] K. Oprzedkiewicz:Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 66(3), (2018), 249–255, DOI: 10.24425/122105.
[20] K. Oprzedkiewicz: Non integer order, state space model of heat transfer process using Atangana-Baleanu operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 68(1), (2020), 43–50, DOI: 10.24425/bpasts.2020.131828.
[21] K. Oprzedkiewicz: Positivity problem for the one dimensional heat transfer process. ISA Transactions, 112, (2021), 281-291 DOI: .
[22] K. Oprzedkiewicz: Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 69(1), (2021), 1–10, DOI: 10.24425/bpasts.2021.135843.
[23] K. Oprzedkiewicz, K. Dziedzic, and Ł. Wi˛ eckowski: Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 67(5), (2019), 905–914, DOI: 10.24425/bpasts.2019.130873.
[24] K. Oprzedkiewicz and E. Gawin: A non-integer order, state space model for one dimensional heat transfer process. Archives of Control Sciences, 26(2), (2016), 261–275, DOI: 10.1515/acsc-2016-0015.
[25] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Modeling heat distribution with the use of a non-integer order, state space model. International Journal of Applied Mathematics and Computer Science, 26(4), (2016), 749– 756, DOI: 10.1515/amcs-2016-0052.
[26] K. Oprzedkiewicz and W. Mitkowski: A memory-efficient nonintegerorder discrete-time state-space model of a heat transfer process. International Journal of Applied Mathematics and Computer Science, 28(4), (2018), 649–659, DOI: 10.2478/amcs-2018-0050.
[27] K. Oprzedkiewicz,W. Mitkowski, E.Gawin, and K. Dziedzic: The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process. Bulletin of the Polish Academy of Sciences. Technical Sciences, 66(4), (2018), 501– 507, DOI: 10.24425/124267.
[28] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Parameter identification for non integer order, state space models of heat plant. In MMAR 2016: 21th international conference on Methods and Models in Automation and Robotics: 29 August–01 September 2016, Międzyzdroje, Poland, pages 184– 188, 2016.
[29] P. Ostalczyk: Discrete Fractional Calculus. Applications in Control and Image Processing. Worlsd Scientific Publishing, Singapore, 2016.
[30] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1999.
[31] G. Recktenwald: Finite-difference approximations to the heat equation. 2011.
[32] M. Rozanski: Determinants of two kinds of matrices whose elements involve sine functions. Open Mathematics, 17(1), (2019), 1332–1339, DOI: 10.1515/math-2019-0096.
[33] N. Al Salti, E. Karimov, and S. Kerbal: Boundary-value problems for fractional heat equation involving caputo-fabrizio derivative. New Trends in Mathematical Sciences, 4(4), (2016), 79–89, arXiv:1603.09471.
[34] D. Sierociuk, T. Skovranek, M. Macias, I. Podlubny, I. Petras, A. Dzielinski, and P. Ziubinski: Diffusion process modeling by using fractional-order models. Applied Mathematics and Computation, 257(1), (2015), 2–11, DOI: 10.1016/j.amc.2014.11.028.
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Authors and Affiliations

Krzysztof Oprzędkiewicz
1
ORCID: ORCID
Klaudia Dziedzic
1

  1. AGH University of Science and Technology in Krakow, Faculty of Electrical Engineering, Automatics, Computer Science and Robotics, Department of Automatics and Biomedical Engineering, Kraków, Poland

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