Details
Title
On controllability of fractional positive continuous-time linear systems with delayJournal title
Archives of Control SciencesYearbook
2021Volume
vol. 31Issue
No 1Affiliation
Sikora, Beata : Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland ; Matlok, Nikola : Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, PolandAuthors
Keywords
fractional systems ; positive systems ; the Caputo derivative ; controllability ; delay ; the Metzler matrixDivisions of PAS
Nauki TechniczneCoverage
29-51Publisher
Committee of Automatic Control and Robotics PASBibliography
[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.