Geodesic
On The Stability of Neutral-type Uncertain Systems With Multiple Time Delays
International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 2, pp. 221-229.

Voir la notice de l'article provenant de la source Library of Science

The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness of the proposed approaches. Compared with results existing in the literature, our methods are shown to be superior to them.
Keywords: Razumikhin-type theorem,, time delay, neutral type uncertain systems
Mots-clés : twierdzenie Razumikhina, opóźnienie czasowe, układ niepewny 
@article{IJAMCS_2005_15_2_a4,
     author = {Liu, P. L.},
     title = {On {The} {Stability} of {Neutral-type} {Uncertain} {Systems} {With} {Multiple} {Time} {Delays}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {221--229},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a4/}
}
TY  - JOUR
AU  - Liu, P. L.
TI  - On The Stability of Neutral-type Uncertain Systems With Multiple Time Delays
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2005
SP  - 221
EP  - 229
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a4/
LA  - en
ID  - IJAMCS_2005_15_2_a4
ER  - 
%0 Journal Article
%A Liu, P. L.
%T On The Stability of Neutral-type Uncertain Systems With Multiple Time Delays
%J International Journal of Applied Mathematics and Computer Science
%D 2005
%P 221-229
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a4/
%G en
%F IJAMCS_2005_15_2_a4
Liu, P. L. On The Stability of Neutral-type Uncertain Systems With Multiple Time Delays. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 2, pp. 221-229. http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_2_a4/

[1] Castelan W.B. and Infante E.F. (1979): A Lyapunov functional for matrix neutral differential equation with one delay. — J. Math. Anal. Appl., Vol. 71, No. 1, pp. 105–130.

[2] Dugard J. and Verriest E.I. (1997): Stability and Control of Time-delay Systems. — New York: Academic Press.

[3] Goubet B., Dambrin M. and Richard J.P. (1997): Stability of perturbed systems with time-varying delays. — Syst. Contr. Lett., Vol. 31, No. 3, pp. 155–163.

[4] Gu K. (1997): Discretized LMI set in the stability problem of linear uncertain time-delay systems.—Int. J. Contr., Vol. 68, No. 4, pp. 923–934.

[5] Gu K. and Niculescu S.I. (2000): Additional dynamics in transformed time-delay systems. — IEEE Trans. Automat. Contr., Vol. AC–45, No. 3, pp. 572–575.

[6] Han Q.L. (2002): Robust stability of uncertain delay-differential systems of neutral type. — Automatica, Vol. 38, No. 4, pp. 719–723.

[7] Han Q.L. (2004): A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. —Automatica, Vol. 40, No. 10, pp. 1791–1796.

[8] He P. and Cao D.Q. (2004): Algebraic stability criteria of linear neutral systems with multiple time delays. — Appl. Math. Comput., Vol. 68, No. 155, pp. 643–653.

[9] He Y., Wu M., She J.H. and Liu G.P. (2004): Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. — Syst. Contr. Lett., Vol. 51, pp. 57–65.

[10] Lien C.H. (1999): Asymptotic criterion for neutral systems with multiple time delays. — Elec. Lett., Vol. 35, pp. 850–852.

[11] Lien C.H. and Fan K.K. (2000): Robust stability for a class of neutral time delay systems. — Proc. Automat. Contr. Conf., Hsinchu, Taiwan, pp. 576–580.

[12] Mahmound M.S. (2000): Robust Control and Filtering for Time-Delay Systems. — New York: Marcel Dekker, Inc.

[13] Niculescu S.I. (2001): Delay Effects in Stability, A Robust Stability Approach. —London: Springer.

[14] Su T.J. and Huang C.G. (1992): Robust stability of delay dependence for linear uncertain systems. — IEEE Trans. Automat. Contr., Vol. AC–37, No. 10, pp. 1656–1659.

[15] Yan J.T. (2000): Robust stability analysis of uncertain time delay systems with delay-dependence. —Elec. Lett., Vol. 37, No. 2, pp. 135–137.

[16] Yang M.S. and Liu P.L. (2002): On asymptotic stability of linear neutral delay-differential systems. — Int. J. Syst. Sci., Vol. 33, No. 11, pp. 901–907.