Decentralized stabilization of fractional positive descriptor continuous-time linear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.2478/amcs-2018-0010

• Języki publikacji: EN

Abstrakty

EN

A method for decentralized stabilization of fractional positive descriptor linear systems is proposed. Necessary and sufficient conditions for decentralized stabilization of fractional positive descriptor linear systems are established. The efficiency of the proposed method is demonstrated on a numerical example.

Słowa kluczowe

EN

positive system; linear system; continuous-time system; descriptor system; decentralized stabilization

PL

układ dodatni; układ liniowy; układ ciągły; układ deskrypcyjny

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2018
• Tom: Vol. 28, no. 1
• Strony: 135--140
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

• [1] Boyd, S. El Ghaoui, L. Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
• [2] Bru, R., Coll, C. and Sanchez E. (2000). About positively discrete-time singular systems, in M.E. Mastorakis (Ed.), System and Control: Theory and Applications, World Scientific and Engineering Society, Athens, pp. 44–48.
• [3] Bru, R. Coll, C. Romero-Vivo, S. and Sanchez, E. (2003). Some problems about structural properties of positive descriptor systems, in L. Benvennnuti et al. (Eds.), Positive Systems, Lecture Notes in Control and Information Science, Vol. 294, Springer, Berlin, pp. 233–240.
• [4] State, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constructions, SIAM Journal on Applied Mathematics 31(3): 411–425.
• [5] Caputo, M. and Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1(2): 1–13.
• [6] Dai, L. (1989). Singular Control Systems, Springer-Verlag, Berlin.
• [7] Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267–1292.
• [8] Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
• [9] Fahmy, M.M. and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421–1431.
• [10] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems,Wiley, New York, NY.
• [11] Giorgio, G. and Zuccotti, C. (2015). Metzlerian and generalized Metzlerian matrices: Some properties and economic applications, Journal of Mathematics Research 7(2): 42–55.
• [12] Kaczorek, T. (1997). Positive singular discrete time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 45(4): 619–631.
• [13] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
• [14] Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453–458.
• [15] Kaczorek, T. (2011a). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
• [16] Kaczorek, T. (2011b). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 753–761.
• [17] Kaczorek, T. (2012). Positive fractional continuous-time linear systems with singular pencil, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9–12.
• [18] Kaczorek, T. (2013). Application of the Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29–33, DOI: 10.2478/amcs-2013-0003.
• [19] Kaczorek, T. (2014a). Descriptor positive discrete-time and continuous-time nonlinear systems, Proceedings of SPIE 92902Q.
• [20] Kaczorek, T. (2014b). Minimum energy control of fractional descriptor positive discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 24(4): 735–743, DOI: 10.2478/amcs-2014-0054.
• [21] Losada, J. and Nieto, J. (2015). Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications 1(2) 87–92.
• [22] Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
• [23] Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Łódź University of Technology Press, Łódź, (in Polish).
• [24] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
• [25] Sajewski, Ł. (2016a). Descriptor fractional discrete-time linear system and its solution—Comparison of three different methods, in R. Szewczyk et al. (Eds.), Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems & Computing, Vol. 440, Springer, Cham, pp. 37–50.
• [26] Sajewski, Ł. (2016b). Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bulletin of the Polish Academy of Sciences: Technical Science 64(1): 15–20.
• [27] Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103–140.
• [28] Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640–2659.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).