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A Lyapunov functional for a neutral system with a time-varying delay

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Języki publikacji
EN
Abstrakty
EN
The paper presents a method of determining of the Lyapunov functional for a linear neutral system with an interval time-varying delay. The Lyapunov functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the trajectory of the system with a time-varying delay. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
Rocznik
Strony
911--918
Opis fizyczny
Bibliogr. 30 poz., wykr.
Twórcy
autor
  • AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Engineering in Biomedicine, Department of Automatics and Engineering in Biomedicine 30 Mickiewicza Ave., 30-059 Cracow, Poland
Bibliografia
  • [1] E. Fridman, “New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems”, Systems & Control Letters 43, 309-319 (2001).
  • [2] D. Ivanescu, S.I. Niculescu, L. Dugard, J.M. Dion, and E.I. Verriest, “On delay-dependent stability for linear neutral systems”, Automatica 39, 255-261 (2003).
  • [3] Q.L. Han, “On robust stability of neutral systems with timevarying discrete delay and norm-bounded uncertainty”, Automatica 40, 1087-1092 (2004).
  • [4] Q.L. Han, “On stability of linear neutral systems with mixed time delays: a discretised Lyapunov functional approach”, Automatica 41, 1209-1218 (2005).
  • [5] Q.L. Han, “A discrete delay decomposition approach to stability of linear retarded and neutral systems”, Automatica 45, 517-524 (2009).
  • [6] Q.L. Han, “Improved stability criteria and controller design for linear neutral systems”, Automatica 45, 1948-1952 (2009).
  • [7] K. Gu and Y. Liu, “Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations”, Automatica 45, 798-804 (2009).
  • [8] V.L. Kharitonov and A.P. Zhabko, “Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems”, Automatica 39, 15-20 (2003).
  • [9] V.L. Kharitonov, “Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case”, Int. J. Control 78, 783-800 (2005).
  • [10] V.L. Kharitonov, “Lyapunov matrices for a class of neutral type time delay systems”, Int. J. Control 81, 883-893 (2008).
  • [11] Q.L. Han, “A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays”, Automatica 40, 1791-1796 (2004).
  • [12] Q.L. Han, “A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices”, Int. J. Systems Science 36, 469-475 (2005).
  • [13] V.L. Kharitonov and D. Hinrichsen, “Exponential estimates for time delay systems”, Systems & Control Letters 53, 395-405 (2004).
  • [14] V.L. Kharitonov and E. Plischke, “Lyapunov matrices for timedelay systems”, Systems & Control Letters 55, 697-706 (2006).
  • [15] K. Gu, “Discretized LMI set in the stability problem of linear time delay systems”, Int. J. Control 68, 923-934 (1997).
  • [16] Yu.M. Repin, “Quadratic Lyapunov functionals for systems with delay”, Prikl. Mat. Mekh. 29, 564-566 (1965).
  • [17] J. Duda, “Parametric optimization problem for systems with time delay”, PhD Thesis, AGH University of Science and Technology, Cracow, 1986.
  • [18] J. Duda, “Parametric optimization of neutral linear system with respect to the general quadratic performance index”, Archives of Automatics and Telemechanics 33, 448-456 (1988).
  • [19] J. Duda, “Parametric optimization of neutral linear system with two delays with P-controller”, Archives of Control Sciences 21, 363-372 (2011).
  • [20] J. Duda, “Parametric optimization of a neutral system with a P-controller”, Archives Des Sciences 66, 534-543 (2013).
  • [21] J. Duda, “Lyapunov functional for a linear system with two delays both retarded and neutral type”, Archives of Control Sciences 20, 89-98 (2010).
  • [22] H. Górecki and L. Popek, “Parametric optimization problem for control systems with time-delay”, 9th World Congress IFAC IX, CD-ROM (1984).
  • [23] H. Górecki and S. Białas, “Relations between roots and coefficients of the transcendental equations”, Bull. Pol. Ac:. Tech. 58, 631-634 (2010).
  • [24] S. Białas and H. Górecki, “Generalization of Vieta’s formulae to the fractional polynomials, and generalizations the method of Graeffe-Lobachevsky”, Bull. Pol. Ac:. Tech. 58, 625-629 (2010).
  • [25] J. Duda, “Lyapunov functional for a linear system with two delays”, Control and Cybernetics 39, 797-809 (2010).
  • [26] J. Duda, “Lyapunov functional for a system with k-noncommensurate neutral time delays”, Control and Cybernetics 39, 1173-1184 (2010).
  • [27] J. Duda, “Lyapunov functional for a linear system with both lumped and distributed delay”, Control and Cybernetics 40, 73-90 (2011).
  • [28] J. Duda, “Lyapunov functional for a system with a time-varying delay”, Int. J. Applied Mathematics and Computer Science 22 (2), 327-337 (2012).
  • [29] H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, John Wiley & Sons, New York, 1989.
  • [30] J. Klamka, Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht, 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0b64beb3-29b8-4413-a38b-8943b9489c8f
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