Practical stability of positive fractional discrete-time linear systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new concept (notion) of the practical stability of positive fractional discrete-time linear systems is introduced. Necessary and sufficient conditions for the practical stability of the positive fractional systems are established. It is shown that the positive fractional systems are practically unstable if corresponding standard positive fractional systems are asymptotically unstable.

Słowa kluczowe

EN

practical stability; fractional; positive; discrete-time; linear; system; stability test

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2008
• Tom: Vol. 56, nr 4
• Strony: 313--317
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems, Theory and Applications, J. Wiley, New York, 2000.
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [3] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differenctial Equations, Willey, New York, 1993.
• [4] K. Nishimoto, Fractional Calculus, Decartess Press, Koriama, 1984.
• [5] K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
• [6] L. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
• [7] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223–228 (2008).
• [8] T. Kaczorek, “Reachability and controllability to zero of positive fractional discrete-time systems”, Machine Intelligence and Robotics Control 6 (4), (2007).
• [9] P. Ostalczyk, “The non-integer difference of the discrete-time function and its application to the control system synthesis”, Int. J. Syst. Sci. 31 (12), 551–1561 (2000).
• [10] M. Vinagre and V. Feliu, “Modeling and control of dynamic system using fractional calculus: application to electrochemical processes and flexible structures”, Proc. 41st IEEE Conf. Decision and Control NV, 214–239 (2002).
• [11] M.D. Ortigueira, “Fractional discrete-time linear systems”, Proc. IEE-ICASSP 3, 2241–2244 (1997).
• [12] H. Gorecki, Analysis and Synthesis of Control Systems with Delay, WNT, Warszawa, 1997, (in Polish).
• [13] T. Kaczorek, “Choice of the forms of Lyapunov functions for positive 2D Roesser model”, Int. J. Applied Math. and Comp. Scienes 17 (4), 471–475 (2007).
• [14] T. Kaczorek, “Asymptotic stability of positive 1D and 2D linear systems”, Proc. National Conf. of Automation, (2008), (to be published).
• [15] T. Kaczorek, “LMI approach to stability 2D positive systems with delays”, Multidimensional Systems and Signal Processing 18 (3), CD ROM (2008).
• [16] M. Twardy, “An LMI approach to checking stability of 2D positive systems”, Bull. Pol. Ac.: Tech. 55 (4), 379–383 (2007).
• [17] M. Twardy, “On the alternative stability criteria for positive systems”, Bull. Pol. Ac.: Tech. 55 (4), 385–393 (2007).
• [18] M. Busłowicz, “Robust stability of positive discrete-time linear systems with multiple delays with unity rank uncertainty structure or non-negative perturbation matrices”, Bull. Pol. Ac.: Tech. 55 (1), 347–350 (2007).
• [19] M. Busłowicz, “Robust stability of convex combination of two fractional degree characteristic polynomials”, Acta Mechanica et Automatica 2, (2008), (to be published).
• [20] T. Kaczorek, “Reachability and controllability to zero tests for standard and positive fractional discrete-time systems”, J. Automation and System Engineering 2, (2008), (to be published).
• [21] T. Kaczorek, “Reachability and controllability to zero of cone fractional linear systems”, Archives of Control Scienes 17 (3), 357–367 (2007).
• [22] J. Klamka, “Positive controllability of positive systems”, Proc. of American Control Conference, ACC-2002, CD-ROM (2002).
• [23] A. Oustalup, Commande CRONE, Hermes, Paris, 1983.
• [24] D. Sierociuk and D. Dzielinski, “Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation”, Int. J. Appl. Math. Comp. Sci. 16 (1), 129–140 (2006).
• [25] K. Gałkowski, A. Kummert, “Fractional polynomials and nD systems”, Proc IEEE Int. Symp. Circuits and Systems ISCAS, CD-ROM (2005).
• [26] T. Kaczorek, “Fractional 2D linear systems”, J. Automation, Mobile Robotics and Intelligent Systems 2 (2), 5–9 (2008).
• [27] T. Kaczorek, “Positive different orders fractional 2D linear systems”, Acta Mechanica et Automatica, (2008), (to be published). Bull. Pol. Ac.: Tech. 56(4) 2008 317