A Lyapunov functional for a system with both lumped and distributed delay

• Autorzy: Duda J.

Identyfikatory

DOI

10.1515/acsc-2017-0031

• Języki publikacji: EN

Abstrakty

EN

In the paper construction of a Lyapunov functional for time delay system with both lumped and distributed delay is presented. The Lyapunov functional is determined by means of the Lyapunov matrix. The method of determination of the Lyapunov matrix for time delay system with both lumped and distributed delay is presented. It is given the example illustrating the method.

Słowa kluczowe

EN

time-delay system; Lyapunov matrix; Lyapunov functional

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2017
• Tom: Vol. 27, no. 4
• Strony: 527--540
• Opis fizyczny: Bibliogr. 32 poz., wykr., wzory

Twórcy

autor

Duda J.

• Department of Automatics and Biomedical Engineering, AGH University of Science and Technology, Krakow, Poland

Bibliografia

• [1] R. Bellman, and K. Cooke: Differential-difference Equations. New York, Academic Press, 1963.
• [2] S. Białas and H. Górecki: Generalization of Vieta’s formulae to the fractional polynomials, and generalizations the method of Graeffe-Lobachevsky. Bulletin of the Polish Academy of Sciences Technical Sciences, 58 (2010), 625-629.
• [3] J. Duda: Lyapunov functional for a linear system with two delays. Control and Cybernetics, 39 (2010), 797-809.
• [4] J. Duda: Lyapunov functional for a system with k-non-commensurate neutral time delays. Control and Cybernetics, 39 (2010), 1173-1184.
• [5] J. Duda: A Lyapunov functional for a neutral system with a time-varying delay. Bulletin of the Polish Academy of Sciences Technical Sciences, 61 (2013), 911-918.
• [6] J. Duda: Lyapunov matrices approach to the parametric optimization of time-delay systems. Archives of Control Sciences, 25 (2015), 279-288.
• [7] J. Duda: Lyapunov matrices approach to the parametric optimization of a neutral system. Archives of Control Sciences, 26 (2016), 81-93.
• [8] J. Duda: Lyapunov matrices approach to the parametric optimization of a system with two delays. Archives of Control Sciences, 26 (2016), 281-295.
• [9] J. Duda: A Lyapunov functional for a neutral system with a distributed time delay. Mathematics and Computers in Simulation, 119 (2016), 171-181.
• [10] J. Duda: Lyapunov matrices approach to the parametric optimization of a neutral system with two delays. Mathematics and Computers in Simulation, 136 (2017), 22-35.
• [11] E. Fridman: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems & Control Letters, 43 (2001), 309-319.
• [12] H. Górecki and S.Białas: Relations between roots and coefficients of the transcendental equations. Bulletin of the Polish Academy of Sciences Technical Sciences, 58 (2010), 631-634.
• [13] H. Górecki, S. Fuksa, P. Grabowski and A. Korytowski: Analysis and Synthesis of Time Delay Systems. John Wiley & Sons. Chichester, New York, Brisbane, Toronto, Singapore, 1989.
• [14] H. Górecki and L. Popek: Parametric optimization problem for control systems with time-delay. 9th World Congress of IFAC IX, CD-ROM, (1984).
• [15] K. Gu: Discretized LMI set in the Stability Problem of Linear Time Delay Systems. Int. J. of Control, 68 (1997), 923-934.
• [16] K. Gu and Y. Liu: Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations. Automatica, 45 (2009), 798-804.
• [17] Q. L. Han: On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty. Automatica, 40 (2004), 1087-1092.
• [18] Q. L. Han: A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica, 40 (2004), 1791-1796.
• [19] Q. L. Han: On stability of linear neutral systems with mixed time delays: A discretised Lyapunov functional approach. Automatica 41 (2005), 1209-1218.
• [20] Q. L. Han: A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. Int. J. of Systems Science, 36 (2005), 469-475.
• [21] Q. L. Han: A discrete delay decomposition approach to stability of linear retarded and neutral systems. Automatica, 45 (2009), 517-524.
• [22] Q. L. Han: Improved stability criteria and controller design for linear neutral systems. Automatica, 45 (2009), 1948-1952.
• [23] 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.
• [24] V. L. Kharitonov: Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case. Int. J. of Control, 78 (2005), 783-800.
• [25] V. L. Kharitonov: Lyapunov matrices for a class of time delay systems. Systems & Control Letters, 55 (2006), 610-617.
• [26] V. L. Kharitonov: Lyapunov matrices for a class of neutral type time delay systems. Int. J. of Control, 81 (2008), 883-893.
• [27] V. L. Kharitonov: On the uniqueness of Lyapunov matrices for a time-delay system. Systems & Control Letters, 61 (2012), 397-402.
• [28] V. L. Kharitonov and D. Hinrichsen: Exponential estimates for time delay systems. Systems & Control Letters, 53 (2004), 395-405.
• [29] V. L. Kharitonov and E. Plischke: Lyapunov matrices for time-delay systems. Systems & Control Letters, 55 (2006), 697-706.
• [30] V. L. Kharitonov and A. P. Zhabko: Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39 (2003), 15-20.
• [31] J. Klamka: Controllability of Dynamical Systems. Kluwer Academic Publishers Dordrecht, 1991.
• [32] Yu and M. Repin: Quadratic Lyapunov functionals for systems with delay. Prikl. Mat. Mekh., 29 (1965), 564-566.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).