Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.
Rocznik
Tom
Strony
709--714
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
- Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok Poland
Bibliografia
- [1] M. Dodig and M. Stosic, “Singular systems state feedbacks problems,” Linear Algebra and its Applications, 431 (8), 1267‒1292 (2009).
- [2] M.M. Fahmy and J. O’Reill, “Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment”, Int. J. Control, 49 (4), 1421‒1431 (1989).
- [3] T. Kaczorek, “Decentralized stabilization of fractional positive descriptor discrete-time linear systems”, Conf. 9th International conference on non-integer order calculus and its applications (to be published).
- [4] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
- [5] E. Virnik, “Stability analysis of positive descriptor systems,” Linear Algebra and its Applications, 429, 2640‒2659 (2008).
- [6] R. Bru, C. Coll, S. Romero-Vivo, and E. Sanchez, “Some problems about structural properties of positive descriptor systems,” in Positive Systems, vol. 294, pp. 233‒240, eds. L. Benvenuti, A. De Santis, L. Farina, Lecture Notes in Control and Information Science, Springer, Berlin, 2003.
- [7] R. Bru, C. Coll, and E. Sanchez, “About positively discrete-time singular systems,” in System and Control: theory and applications, pp. 44‒48, eds. M.E. Mastorakis, World Scientific and Engineering Society, Athens, 2000.
- [8] L. Farina and S. Rinaldi, Positive Linear Systems, J. Wiley, New York, 2000.
- [9] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London 2002.
- [10] L. Dai, Singular Control Systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.
- [11] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
- [12] T. Kaczorek, “Descriptor fractional linear systems with regular pencils,” Int. J. Appl. Math. Comput. Sci. 23 (2), 309‒315 (2013).
- [13] T. Kaczorek, “Singular fractional continuous-time and discrete- time linear systems,” Acta Mechanica et Automatica 7 (1), 26‒33 (2013).
- [14] K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York 1974.
- [15] P. Ostalczyk, Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Wydawnictwo Politechniki Łódzkiej, Łódź, 2008 [in Polish].
- [16] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
- [17] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Ultracapacitor parameters identification based on fractional order model”, Proc. of European Control Conference, Budapest, 196‒200 (2009).
- [18] N.M.F. Ferreira and J.A.T Machado, “Fractional-order hybrid control of robotic manipulators”, Proc. of 11th Int. Conf. Advanced Robotics, Coimbra, Portugal, 393‒398 (2003).
- [19] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
- [20] G.R. Duan, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
- [21] T. Kaczorek, “Positive linear systems with different fractional orders,” Bull. Pol. Ac.: Tech. 58 (3), 453‒458 (2010).
- [22] 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).
- [23] T. Kaczorek, “Solution of the state equations of descriptor fractional discrete-time linear systems with regular pencils”, Tech. Transp. Szyn. 10, 415‒422 (2013).
- [24] Ł. Sajewski, “Descriptor fractional discrete-time linear system and its solution – comparison of three different methods”, in Challenges in Automation, Robotics and Measurement Techniques, vol. 440, 37‒50, eds. Szewczyk et al., Advances in Intelligent Systems and Computing, Springer, Cham, 2016.
- [25] Ł. Sajewski, “Descriptor fractional discrete-time linear system with two different fractional orders and its solution”, Bull. Pol. Ac.: Tech. 64 (1), 15‒20 (2016).
- [26] T. Kaczorek “Practical stability of positive fractional discrete-time linear systems”, Bull. Pol. Ac.: Tech. 56 (4), 313‒317 (2010).
- [27] T. Kaczorek, “Tests for practical stability of positive fractional discrete-time linear systems”, Measurements, Automation Robotics 14 (2), 463‒469 (2010).
- [28] M. Busłowicz and A. Ruszewski, “Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems,” Bull. Pol. Ac.: Tech. 61 (4), 779‒786 (2013).
- [29] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, 1994.
- [30] G. Giorgio and C. Zuccotti, “Metzlerian and generalized Metzlerian matrices: Some properties and economic applications”, Journal of Mathematics Research, 7 (2), 42‒55 (2015).
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-94cfbac8-3e0c-4913-8946-c27d4145b9fb