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2012 | 22 | 2 | 327-337
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
Słowa kluczowe
Rocznik
Tom
22
Numer
2
Strony
327-337
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-01-27
poprawiono
2011-05-26
poprawiono
2011-08-01
Twórcy
autor
  • Department of Automatics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland
Bibliografia
  • Duda, J. (1986). Parametric Optimization Problem for Systems with Time Delay, Ph.D. thesis, AGH University of Science and Technology, Cracow.
  • 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. (2010a). Lyapunov functional for a linear system with two delays, Control & Cybernetics 39(3): 797-809.
  • Duda, J. (2010b). Lyapunov functional for a linear system with two delays both retarded and neutral type, Archives of Control Sciences 20(LVI): 89-98.
  • Fridman, E. (2001). New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems & Control Letters 43(4): 309-319.
  • Górecki, H., Fuksa, S., Grabowski, P., Korytowski, A. (1989). Analysis and Synthesis of Time Delay Systems, John Wiley & Sons, Chichester/New York, NY/Brisbane/Toronto/Singapore.
  • Gu, K. (1997). Discretized LMI set in the stability problem of linear time delay systems, International Journal of Control 68(4): 923-934.
  • Gu, K. and Liu, Y. (2009). Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica 45(3): 798-804.
  • Han, Q.L. (2004). On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica 40(6): 1087-1092.
  • Han, Q.L. (2004). A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, Automatica 40(10): 1791-1796.
  • Han, Q.L. (2005). On stability of linear neutral systems with mixed time delays: A discretised Lyapunov functional approach, Automatica 41(7): 1209-1218.
  • Han, Q.L. (2009). A discrete delay decomposition approach to stability of linear retarded and neutral systems, Automatica 45(2): 517-524.
  • Infante, E.F. and Castelan, W.B. (1978). A Lyapunov functional for a matrix difference-differential equation, Journal of 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(2): 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(5): 395-405.
  • Kharitonov, V.L. and Plischke, E. (2006). Lyapunov matrices for time-delay systems, Systems & Control Letters 55(9): 697-706.
  • Kharitonov, V.L., Zhabko, A.P. (2003). Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems, Automatica 39(1): 15-20.
  • Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht.
  • Repin, Yu. M. (1965). Quadratic Lyapunov functionals for systems with delay, Prikladnaja Matiematika i Miechanika 29: 564-566.
  • Respondek, J.S. (2008). Approximate controllability of the n-th order infinite dimensional systems with controls delayed by the control devices, International Journal of Systems Science 39(8): 765-782.
  • Richard, J.P. (2003). Time-delay systems: An overview of some recent advances and open problems, Automatica 39(10): 1667-1694.
  • Wang, D., Wang, W. and Shi, P. (2009). Exponential H-infinity filtering for switched linear systems with interval timevarying delay, International Journal of Robust and Nonlinear Control 19(5): 532-551.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv22i2p327bwm
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