Stability of fractional positive nonlinear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/acsc-2015-0031

• Języki publikacji: EN

Abstrakty

EN

The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.

Słowa kluczowe

EN

positive; fractional; nonlinear; system; stability

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2015
• Tom: Vol. 25, no. 4
• Strony: 491--496
• Opis fizyczny: Bibliogr. 18 poz., wykr., wzory

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] A. Berman and R. J. Plemmons: Nonegative Matrices in the Mathematical Sciences. SIAM, 1994.
• [2] M. Busłowicz: Stability of linear continuous-time fractional order systems with delays of the retarded type. Bulletin of the Polish Academy of Sciences: Technical Sciences, 56(4), (2008), 319-324.
• [3] M. Busłowicz: Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders. Bulletin of the Polish Academy of Sciences: Technical Sciences, 60(2), (2012), 279-284.
• [4] M. Busłowicz and T. Kaczorek: Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. of Applied Mathematics and Computer Science, 19(2), (2009), 263-169.
• [5] L. Farina and S. Rinaldi: Positive Linear Systems; Theory and Applications. J. Wiley, New York, 2000.
• [6] T. Kaczorek: Approximation of positive stable continuous-time linear systems by positive stable discrete-time systems. Pomiary Automatyka Robotyka, 2, (2013), 359-364.
• [7] T. Kaczorek: Comparison of approximation methods of positive stable contiunuous- time linear systems by positive stable discrete-time systems. Computer Applications in Electrical Engeenering, Pub. House of Poznan University of Tehnology, Poznań, 2013, 1-10.
• [8] T. Kaczorek: Positive 1D and 2D Systems. Springer Verlag, London, 2002.
• [9] T. Kaczorek: Linear Control Systems. 1, Research Studies Press J. Wiley, New York, 1992.
• [10] T. Kaczorek: Positive linear systems with different fractional orders. Bulletin of the Polish Academy of Sciences: Technical Sciences, 58(3), (2010), 453-458.
• [11] T. Kaczorek: Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils. Int. J. of Applied Mathematics and Computer Science, 23(1), (2013), 29-34.
• [12] T. Kaczorek: Reduction and decomposition of singular fractional discrete-time linear systems. Acta Mechanica et Automatica, 5(4), (2011), 62-66.
• [13] T. Kaczorek: Singular fractional discrete-time linear systems. Control and Cybernetics, 40(3), (2011), 753-761.
• [14] T. Kaczorek: Selected Problems of Fractional System Theory, Springer Verlag, Berlin, 2011.
• [15] T. Kaczorek: Fractional positive continuous-time linear systems and their reachability. Int. J. of Applied Mathematics and Computer Science, 18(2), (2008), 223-228.
• [16] T. Kaczorek: Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. on Circuits and Systems, 58(7), (2011), 1203-1210.
• [17] T. Kaczorek: Positive fractional continuous-time linear systems with singular pencils. Bulletin of the Polish Academy of Sciences: Technical Sciences, 60(1), (2012), 9-12.
• [18] W. Xiang-Jun, W. Zheng-Mao and L. Jun-Guo: Stability analysis of a class of nonlinear fractional-order systems. IEEE Trans. Circuits and Systems-II, Express Briefs, 55(11), (2008), 1178-1182.

Uwagi

EN

This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467