Positivity and stability of fractional discrete-time linear systems. The model without a time shift in the difference

• Autorzy: Kaczorek T. , Ostalczyk P.
• Języki publikacji: EN

Abstrakty

EN

The positivity and stability of fractional discretetime linear systems described by a new model are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the systems are established. New tests for checking of the stability are proposed.

Słowa kluczowe

EN

positivity; stability; fractional discrete-time linear systems

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2017
• Tom: Vol. 46, no. 1
• Strony: 27--36
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology, Faculty of Electrical Engineering Wiejska 45D, 15-351 Bialystok

autor

Ostalczyk P.

• Lodz University of Technology, Institute of Automatic Control Stefanowskiego 18/22, 90-924 Lodz

Bibliografia

• [1] Aracena J., Demongeot J. and Goles E. (2004) Positive and negative circuits in discrete neural networks. IEEE Trans. Neural Networks, 15 (1), 77–83.
• [2] Buslowicz M. (2010) Robust stability of positive discrete-time linear systems of fractional order. Bull. Pol. Acad. Sci. Techn., 58 (4), 567–572.
• [3] Farina L. and Rinaldi S. (2000) Positive Linear Systems; Theory and Applications. J. Wiley, New York. Gantmacher F.R. (1959) The Theory of Matrices. Chelsea Pub. Comp., London.
• [4] Kaczorek T. (2013) Constructibility and observability of standard and positive electrical circuits. Electrical Review, 89(7), 132–136.
• [5] Kaczorek T. (2013) Decoupling zeros of positive electrical circuits. Archives of Electrical Engineering, 62 (4), 553–568.
• [6] Kaczorek T. (2008) Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comput. Sci., 18 (2), 223-228.
• [7] Kaczorek T. (2002) Positive 1D and 2D Systems. Springer-Verlag, London.
• [8] Kaczorek T. (2010) Positive linear systems with different fractional orders. Bull. Pol. Acad. Sci. Techn., 58 (3), 453–458.
• [9] Kaczorek T. (2011a) Positiveelectrical circuits and their reachability. Archives of Electrical Engineering, 60 (3), 283–301.
• [10] Kaczorek T. (2011b) Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems, 58 (6), 1203–1210.
• [11] Kaczorek T. (2011c) Selected Problems of Fractional Systems Theory. SpringerVerlag, Berlin.
• [12] Kaczorek T. (2011d) Singular fractional linear systems and electrical circuits. Int. J. Appl. Math. Comput. Sci., 21 (2), 379–384.
• [13] Kaczorek T. and Ostalczyk P. (2016) Responses comparison of the Two Discrete-Time Linear Fractional State-Space Models. Fractional Calculus and Applied Analysis, 19 (4), 789–805.
• [14] Kaczorek T. and Rogowski K. (2015) Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, 13, Springer.
• [15] Ostalczyk P. (2008) Epitome of the Fractional Calculus: Theory and its Applications in Automatics. Publishing Department of Technical University of Lodz, L odz (in Polish).
• [16] Richard A. (2009) Positive circuits and maximal number of fixed points in discrete dynamical systems. Discrete Applied Mathematics, 157, 3281– 3288.
• [17] Stanislawski R. (2013) Advances in modeling fractional difference systems - new accuracy, stability and computational results. Studia i monografie, issue 343, Politechnika Opolska, Opole.
• [18] Wei R., Tse P.W., Du B., Wang Y. (2016) An innovative fixed-pole numerical approximation for fractional order systems. ISA Transactions, 62, May 2016, 94–102.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).