Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper necessary and sufficient conditions of controllability and observability for solutions of the state equations of fractional continuous time linear systems with regular pencils are proposed. The derivations of the conditions are based on the construction of Gramian matrices.
Rocznik
Tom
Strony
297--304
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
- Centre for Advanced Studies in Pure and Applied Mathematics, BZU, Multan, Pakistan
autor
- Centre for Advanced Studies in Pure and Applied Mathematics, BZU, Multan, Pakistan
autor
- PIET, Multan, Pakistan
Bibliografia
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- [3] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
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- [5] R. Caponetto, G. Dongola, L. Fortuna, I. Petras, Fractional Order Systems Modeling and Control Applications, World Scientific Publishing Co., Taiwan, 2010.
- [6] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Ultracapacitor parameters identification based on fractional order model”, Proc. Eur. Control Conf. (ECC) 1, 196–200 (2009).
- [7] N. M. F. Ferreira and J. A. T Machado, “Fractional-order hybrid control of robotic manipulators”, Proc. 11th Int. Conf. Advanced Robotics, ICAR 1, 393–398 (2003).
- [8] T. Kaczorek, Selected Problems of Fractional Systems Theory, LNCIS Vol. 411. Springer, Heidelberg, 2011.
- [9] J. K. Popović, S. Pilipović, and T. M. Atanacković, “Two compartmental fractional derivative model with fractional derivatives of different order”, Communications in Nonlinear Science and Numerical Simulation 18 (9), 2507–2514 (2013).
- [10] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differenctial Equations, Wiley, New York, 1993.
- [11] C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue, V. Feliu, Fractional-order Systems and Controls; Fundamentals and Applications, Springer, London, 2010.
- [12] S. L. Campbell, C. D. Meyer, and N. J. Rose, “Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients”, SIAM J Appl. Math. 31 (3), 411–425 (1976).
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- [14] M. Dodig and M. Stosic, “Singular systems state feedbacks problems”, Linear Algebra and Its Applications 431 (8), 1267–1292 (2009).
- [15] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
- [16] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor discrete-time linear systems”, Bull. Pol. Ac.: Tech. 64 (2), 395–399, (2016).
- [17] T. Kaczorek, “Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems”, Int. J. Appl. Math. Comput. Sci., 26(2) 277–283 (2016).
- [18] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci., 25(2) 217–221 (2015).
- [19] T. Kaczorek, “Positivity and asymptotic stability of descriptor linear systems with regular pencils”, Archives of Control Sciences, 24(2) 193–205 (2014).
- [20] T. Kaczorek, “Fractional descriptor observers for fractional descriptor continuous-time linear system”, Archives of Control Sciences, 24(1) 27–37 (2014).
- [21] T. Kaczorek, “Descriptor linear fractional linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci., 23(2) 309‒315 (2013).
- [22] T. Kaczorek, “Singular fractional continuous-time and discretetime linear systems”, Acta Mechanica et Automatica 7 (1), 26–33 (2013).
- [23] T. Kaczorek, “Singular fractional discrete-time linear systems”, Control and Cybernetics 40 (3), 1–8 (2011).
- [24] T. Kaczorek, K. Rogowski, “Fractional linear systems and electrical circuits” in Studies in Systems, Decision and Control, vol. 13, (2014).
- [25] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech. 62 (3), 409–412, (2014).
- [26] W. Wülling, “The Drazin inverse of a singular, unreduced tridiagonal matrix”, Linear Algebra Appl., 439 (10) 2736‒2745 (2013).
- [27] T. Berger, T. Reis, “Controllability of linear differential– algebraic systems a survey”, in A. Ilchman & T.Reis (eds.), Surveys in Differential–Algebraic Equations I. Differential– Algebraic Equations Forum, Berlin, Springer 1–61. (2013)
- [28] J. Klamka, Controllability of Dynamical Systems, Kluwer Academic, Dordrecht, 1993.
- [29] J. Wei, “The controllability of fractional control system with control delay”, Computer and Mathematics with Appl. 64(12) 3153–3159 (2012).
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Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-71bd07e5-75d8-4ffe-816e-08f0fd1af5b7