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

International Journal of Applied Mathematics and Computer Science (2012)

- Volume: 22, Issue: 2, page 327-337
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topJózef Duda. "A Lyapunov functional for a system with a time-varying delay." International Journal of Applied Mathematics and Computer Science 22.2 (2012): 327-337. <http://eudml.org/doc/208111>.

@article{JózefDuda2012,

abstract = {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.},

author = {Józef Duda},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Lyapunov functional; time delay system; LTI system},

language = {eng},

number = {2},

pages = {327-337},

title = {A Lyapunov functional for a system with a time-varying delay},

url = {http://eudml.org/doc/208111},

volume = {22},

year = {2012},

}

TY - JOUR

AU - Józef Duda

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2012

VL - 22

IS - 2

SP - 327

EP - 337

AB - 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.

LA - eng

KW - Lyapunov functional; time delay system; LTI system

UR - http://eudml.org/doc/208111

ER -

## References

top- 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. Zbl0696.34051
- Duda, J. (2010a). Lyapunov functional for a linear system with two delays, Control & Cybernetics 39(3): 797-809. Zbl1280.93036
- 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. Zbl1219.93089
- Fridman, E. (2001). New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems & Control Letters 43(4): 309-319. Zbl0974.93028
- 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. Zbl0695.93002
- Gu, K. (1997). Discretized LMI set in the stability problem of linear time delay systems, International Journal of Control 68(4): 923-934. Zbl0986.93061
- Gu, K. and Liu, Y. (2009). Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica 45(3): 798-804. Zbl1168.93384
- Han, Q.L. (2004). On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica 40(6): 1087-1092. Zbl1073.93043
- 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. Zbl1075.93032
- Han, Q.L. (2005). On stability of linear neutral systems with mixed time delays: A discretised Lyapunov functional approach, Automatica 41(7): 1209-1218. Zbl1091.34041
- Han, Q.L. (2009). A discrete delay decomposition approach to stability of linear retarded and neutral systems, Automatica 45(2): 517-524. Zbl1158.93385
- Infante, E.F. and Castelan, W.B. (1978). A Lyapunov functional for a matrix difference-differential equation, Journal of Differential Equations 29: 439-451. Zbl0354.34049
- 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. Zbl1011.93062
- 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. Zbl1097.93027
- Kharitonov, V.L. (2008). Lyapunov matrices for a class of neutral type time delay systems, International Journal of Control 81(6): 883-893. Zbl1152.34375
- Kharitonov, V.L. and Hinrichsen, D. (2004). Exponential estimates for time delay systems, Systems & Control Letters 53(5): 395-405. Zbl1157.34355
- Kharitonov, V.L. and Plischke, E. (2006). Lyapunov matrices for time-delay systems, Systems & Control Letters 55(9): 697-706. Zbl1100.93045
- Kharitonov, V.L., Zhabko, A.P. (2003). Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems, Automatica 39(1): 15-20. Zbl1014.93031
- Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht. Zbl0732.93008
- 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. Zbl1283.93054
- Richard, J.P. (2003). Time-delay systems: An overview of some recent advances and open problems, Automatica 39(10): 1667-1694. Zbl1145.93302
- 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. Zbl1160.93328

## Citations in EuDML Documents

top- Máximo Ramírez, Raúl Villafuerte, Temoatzin González, Miguel Bernal, Exponential estimates of a class of time-delay nonlinear systems with convex representations
- Qiaoling Chen, Zhidong Teng, Zengyun Hu, Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.