Simple analytic conditions for stability of fractional discrete-time linear systems with diagonal state matrix

• Autorzy: Busłowicz M.
• Języki publikacji: EN

Abstrakty

EN

In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems with a diagonal state matrix are addressed. Standard and positive systems are considered. Simple necessary and sufficient analytic conditions for practical stability and for asymptotic stability are established. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

linear system; discrete-time; fractional; practical stability; asymptotic stability

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2012
• Tom: Vol. 60, nr 4
• Strony: 809--814
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Busłowicz M.

• Białystok University of Technology, Faculty of Electrical Engineering, 45D Wiejska St., 15-351 Białystok, Poland

Bibliografia

• [1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
• [2] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applicationsof Fractional Differential Equations, Elsevier, Amsterdam, 2006.
• [3] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
• [4] H. Sheng, Y. Chen, and T. Qiu, Fractional Processes andFractional-Order Signal Processing, Springer, London, 2012.
• [5] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits andSystems - I: Regular papers, 58 (7), 1203-1210 (2011).
• [6] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Some applications of fractional order calculus”, Bull. Pol. Ac.: Tech. 58, 583-592 (2010).
• [7] R. Stanisławski, W.P. Hunek, and K.J. Latawiec, “Normalized finite fractional discrete-time derivative - a new concept and its application to OBF modeling”, Measurement Automationand Monitoring 57, 142-145 (2011).
• [8] J. Klamka, “Local controllability of fractional discrete-time nonlinear systems with delay in control”, in Advances in ControlTheory and Automation, eds. M. Busłowicz and K. Malinowski, pp. 25-34, Printing House of Białystok University of Technology, Białystok, 2012.
• [9] M. Busłowicz, “Stability of linear continuous-time fractional order systems with delays of the retarded type”, Bull. Pol. Ac.:Tech. 56, 319-324 (2008).
• [10] I. Petras, “Stability of fractional-order systems with rational orders: a survey”, Fractional Calculus & Applied Analysis. Int. J. Theory and Applications 12, 269-298 (2009).
• [11] M. Busłowicz, “Stability analysis of linear continuous-time fractional systems of commensurate order”, J. Automation, MobileRobotics and Intelligent Systems 3, 16-21 (2009).
• [12] M. Busłowicz, “Stability of state-space models of linear continuous-time fractional order systems”, Acta Mechanica etAutomatica 5, 15-22 (2011).
• [13] M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders”, Bull. Pol. Ac.: Tech. 60, 279-284 (2012).
• [14] J. Sabatier, M. Moze, and C. Farges, “LMI stability conditions for fractional order systems”, Computers and Mathematics withApplications 59, 1594-1609 (2010).
• [15] M.S. Tavazoei and M. Haeri, “Note on the stability of fractional order systems”, Mathematics and Computers in Simulation 79, 1566-1576 (2009).
• [16] A. Dzieliński and D. Sierociuk, “Stability of discrete fractional order state-space systems”, J. Vibration and Control 14, 1543-1556 (2008).
• [17] M. Busłowicz, “Practical stability of scalar discrete-time linear systems of fractional order”, in Automation of DiscreteProcesses: Theory and Applications, eds. A. Świerniak and J. Krystek, vol. 1, pp. 31-40, Printing House of Silesian University of Technology, Gliwice, 2012, (in Polish).
• [18] S. Guermah, S. Djennoune, and M. Bettayeb, “A new approach for stability analysis of linear discrete-time fractional-order systems”, in: New Trends in Nanotechnology and FractionalCalculus Applications, ed. D. Baleanu, pp. 151-162, Springer, Berlin, 2010.
• [19] T. Kaczorek, “Practical stability of positive fractional discretetime systems”, Bull. Pol. Ac.: Tech. 56, 313-317 (2008).
• [20] M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of linear positive fractional discrete-time linear systems”, Int. J. Applied Mathematics and Computer Science 19, 263-269 (2009).
• [21] M. Busłowicz, „Practical robust stability of positive fractional scalar discrete-time systems”, Silesian University of TechnologyScientific Notebooks. Automatics 151, 24-30 (2008), (in Polish).
• [22] T. Kaczorek, Polynomial and Rational Matrices, Applicationsin Dynamical Systems Theory, Springer, London, 2007.
• [23] E.N. Gryazina, B.T. Polyak, and A.A. Tremba, “Ddecomposition technique state-of-the-art”, Automation and RemoteControl 69, 1991-2026 (2008).
• [24] J. Ackermann, Sampled-data Control Systems, Springer, Berlin, 1985.