Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The paper presents a method of determining of the Lyapunov quadratic functional for linear time-invariant system with two delays both retarded and neutral type. The Lyapunov functional is constructed for a given its time derivative which is calculated on the trajectory of the system with two delays both retarded and neutral type. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
89--98
Opis fizyczny
Bibliogr. 19 poz., wzory
Twórcy
autor
- Institute of Automatic Control, AGH University of Science and Technology, Krakow, Poland, jduda@agh.edu.pl
Bibliografia
- [1] J. DUDA: Parametric optimization problem for systems with time delay. PhD thesis, AGH University of Science and Technology, Krakow, Poland, 1986.
- [2] J. DUDA: Parametric optimization of neutral linear system with respect to the general quadratic performance index. Archiwum Automatyki i Telemechaniki, 33 (1988), 448-456.
- [3] J. DUDA: Lyapunov functional for a linear system with two delays. Control and Cybernetics, (2009), in press.
- [4] E. FRIDMAN: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters, 43 (2001), 309-319.
- [5] H. GO RECKI, S. FUKSA, P. G RABOWSKI and A. KORYTOWSKI: Analysis and synthesis of time delay systems. John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore, (1989).
- [6] K. Gu: Discretized LMI set in the stability problem of linear time delay systems. Int. J. of Control, 68 (1997), 923-934.
- [7] K. Gu and Y. Liu: Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations. Automatica, 45 (2009), 798-804.
- [8] Q. L. HAN: On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty. Automatica. 40 (2004), 1087-1092.
- [9] Q. L. HAN: A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica, 40 (2004), 1791-1796.
- [10] Q. L. HAN: On stability of linear neutral systems with mixed time delays: A discretised Lyapunov functional approach. Automatica, 41 (2005), 1209-1218.
- [11] Q. L. HAN: Discrete delay decomposition approach to stability of linear retarded and neutral system. Automatica, 45 (2009), 517-524.
- [12] E. F. INFANTE and W. B. C ASTELAN: A Liapunov functional for a matrix difference-differential equation. J. Differential Equations, 29 (1978), 439-451.
- [13] D. IVANESCU, S. I. NICULESCU, L. DUGARD, J. M. DION, and E. I. VERRIEST: On delay-dependent stability for linear neutral systems. Automatica, 39 (2003), 255-261.
- [14] V. L. KHARITONOV: Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case. Jut. J. of Control, 78 (2005), 783-800.
- [15] V. L. KHARITONOV: Lyapunov matrices for a class of neutral type time delay systems. Int. J. of Control, 81 (2008), 883-893.
- [16] V. L. KHARITONOV and D. HINRICHSEN: Exponential estimates for time delay systems. Systems & Control Letters, 53 (2004), 395-405.
- [17] V. L. KHARITONOV and E. PLISCHKE: Lyapunov matrices for time-delay systems. Systems & Control Letters, 55 (2006), 697-706.
- [18] V. L. KHARITONOV and A. P. ZHABKO: Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39 (2003), 15-20.
- [19] Yu. M. REPIN: Quadratic Lyapunov functionals for systems with delay. Prikl. Mat. Mekh., 29 (1965), 564-566.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0064-0006