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Lyapunov functional for a system with k-non-commensurate neutral time delays

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Języki publikacji
EN
Abstrakty
EN
The paper presents a method of determining the Lyapunov quadratic functional for linear time-invariant system with k-non-commensurate neutral type time delays. The Lyapunov functional is constructed for its given time derivative, which is calculated on the trajectory of the system with k-non-commensurate neutral type time delays. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
Rocznik
Strony
1173--1184
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Institute of Automatic Control AGH University of Science and Technology, Cracow, Poland
Bibliografia
  • DUDA, J. (1986) Parametric optimization problem for systems with time delay. PhD thesis, AGH University of Science and Technology, Poland.
  • DUDA, J. (1988) Parametric optimization of neutral linear system with respect to the general quadratic performance index. Archiwum Automatyki i Telemechaniki, 33(3), 448-456.
  • DUDA, J. (2010) Lyapunov functional for a linear system with two delays. Control & Cybernetics, 39(3).
  • FRIDMAN, E. (2001) New Lyapunov-Krasovskii functional for stability of linear retarded and neutral type systems. Systems & Control Letters, 43, 309-319.
  • GÓRECKI, H., FUKSA, S., GRABOWSKI, P. and KORYTOWSKI, A. (1989) Analysis and Synthesis of Time Delay Systems. John Wiley & Sons, Chichester-New York-Brisbane-Toronto-Singapore.
  • GU, K. (1997) Discretized LMI set in the Stability Problem of Linear Time Delay Systems. International Journal of Control, 68, 923-934.
  • GU, K. and LIU, Y. (2009) Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations. Automatica, 45, 798-804.
  • HAN, Q.L. (2004) On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty. Automatica, 40,1087-1092.
  • HAN, Q.L. (2004) A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica, 40, 1791-1796.
  • HAN, Q.L. (2005a) A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469-475.
  • HAN, Q.L. (2005b) On stability of linear neutral systems with mixed time delays: A discretised Lyapunov functional approach. Automatica, 41, 1209-1218.
  • HAN, Q.L. (2009a) A discrete delay decomposition approach to stability of linear retarded and neutral systems. Automatica, 45, 517-524.
  • HAN, Q.L. (2009b) Improved stability criteria and controller design for linear neutral systems. Automatica, 45, 1948-1952.
  • INFANTE, E.F. and CASTELAN, W.B. (1978) A Liapunov Functional For a Matrix Difference-Differential Equation. J. Differential Equations, 29, 439-451.
  • IVANESCU, D., NICULESCU, S.I., DUGARD, L., DION, J.M. and VERRIEST, E.I. (2003) On delay-dependent stability for linear neutral systems. Automatica, 39, 255-261.
  • KHARITONOV, V.L. (2005) Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case. International Journal of Control, 78(11), 783-800.
  • KHARITONOV, V.L. (2008) Lyapunov matrices for a class of neutral type time delay systems. International Journal of Control, 81(6), 883-893.
  • KHARITONOV, V.L. and HINRICHSEN, D. (2004) Exponential estimates for time delay systems. Systems & Control Letters, 53, 395-405.
  • KHARITONOV, V.L. and PLISCHKE, E. (2006) Lyapunov matrices for time-delay systems. Systems & Control Letters, 55, 697-706.
  • KHARITONOV, V.L. and ZHABKO, A.P. (2003) Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39, 15-20.
  • KLAMKA, J. (1991) Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht.
  • REPIN, Yu.M. (1965) Quadratic Lyapunov functionals for systems with delay. Prikl. Mat. Mekh., 29, 564-566.
  • RICHARD, J.P. (2003) Time-delay systems: an overview of some recent advances and open problems. Automatica, 39, 1667-1694.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0060-0020
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