zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On delay-dependent robust stability of a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays. (English) Zbl 1202.93105
Summary: This paper deals with the problem of a new delay-dependent robust stability criteria for a class of mixed neutral and Lur’e systems. The system has time-varying uncertainties, interval time-varying delays and sector-bounded nonlinearity. The proposed method is based on Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of linear matrix inequality. Numerical examples show the effectiveness of the proposed method.
MSC:
93D09Robust stability of control systems
93D20Asymptotic stability of control systems
93C10Nonlinear control systems
34H05ODE in connection with control problems
Software:
LMI toolbox
References:
[1]Lur’e, A. I.: Some nonlinear problem in the theory of automatic control, (1957)
[2]Cao, J.; Zhong, S.: New delay-dependent condition for absolute stability of lurie control systems with multiple time-delays and nonlinearities, Appl. math. Comput. 194, 250-258 (2007) · Zbl 1193.93143 · doi:10.1016/j.amc.2007.04.034
[3]Souza, F. O.; Palhares, R. M.; Mendes, E. M. A.M.; Torres, L. A. B.: Control for master–slave synchronization of Lur’e systems with time-delay feedback control, Int. J. Bifur. chaos 18, No. 4, 1161-1173 (2008) · Zbl 1147.93328 · doi:10.1142/S0218127408020896
[4]Souza, F. O.; Palhares, R. M.; Torres, L. A. B.; Mendes, E. M. A.M.: Further results on master–slave synchronization of general Lur’e systems with time-varying delay, Int. J. Bifur. chaos 18, No. 1, 187-202 (2008) · Zbl 1146.93031 · doi:10.1142/S0218127408020227
[5]Cao, J.; Zhong, S.; Hu, Y.: Delay-dependent condition for absolute stability of lurie control systems with multiple time delays and nonlinearities, J. math. Anal. appl. 338, 497-504 (2008) · Zbl 1136.93028 · doi:10.1016/j.jmaa.2007.05.039
[6]Souza, F. O.; Palhares, R. M.; Leite, V. J. S.: Improved robust control for neutral systems via discretised Lyapunov–Krasovskiĭ functional, Int. J. Control 81, No. 9, 1462-1474 (2008) · Zbl 1152.93364 · doi:10.1080/00207170701867410
[7]Han, Q. L.: A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems, Automatica 44, 272-277 (2008) · Zbl 1138.93039 · doi:10.1016/j.automatica.2007.04.009
[8]Yu, K. -W.; Lien, C. -H.: Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos solitons fractals 38, 650-657 (2008) · Zbl 1146.93366 · doi:10.1016/j.chaos.2007.01.002
[9]Wu, L.; Wang, C.; Zeng, Q.: Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems, J. franklin inst. 345, 233-253 (2008) · Zbl 1167.93326 · doi:10.1016/j.jfranklin.2007.09.001
[10]Park, P. G.: A delay-dependent stability criterion for systems with uncertain linear state-delayed systems, IEEE trans. Autom. control 35, 876-877 (1999) · Zbl 0957.34069 · doi:10.1109/9.754838
[11]Park, J. H.; Won, S.: A note on stability of neutral delay-differential systems, J. franklin inst. 336, 543-548 (1999) · Zbl 0969.34066 · doi:10.1016/S0016-0032(98)00040-4
[12]Fridman, E.; Shaked, U.: An improved stabilization method for linear time-delay systems, IEEE trans. Autom. control 47, No. 2, 1931-1937 (2002)
[13]Fridman, E.; Shaked, U.: Control of linear state-delay descriptor systems: an LMI approach, Linear algebra appl. 351–352, 271-302 (2002) · Zbl 1006.93021 · doi:10.1016/S0024-3795(01)00563-8
[14]Cao, J.; Zhong, S.; Hu, Y.: Global stability analysis for a class of neutral networks with varying delays and control input, Appl. math. Comput. 189, 1480-1490 (2007) · Zbl 1128.34046 · doi:10.1016/j.amc.2006.12.048
[15]Impram, S. T.; Munro, N.: A note on absolute stability of uncertain systems, Automatica 37, 605-610 (2001) · Zbl 0972.93510 · doi:10.1016/S0005-1098(00)00194-1
[16]He, Y.; Wu, M.; She, J. H.; Liu, G. P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Syst. control lett. 51, 57-65 (2004) · Zbl 1157.93467 · doi:10.1016/S0167-6911(03)00207-X
[17]Partington, R. J.; Bonnet, C.: H1 and BIBO stabilization of delay systems of neutral type, Syst. control lett. 52, No. 3–4, 283-288 (2004) · Zbl 1157.93367 · doi:10.1016/j.sysconle.2003.09.014
[18]Han, Q. L.: On robust stability of neutral systems with time-varying delay and norm-bounded uncertainty, Automatica 40, 1087-1092 (2004) · Zbl 1073.93043 · doi:10.1016/j.automatica.2004.01.007
[19]Park, J. H.: Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations, Appl. math. Comput. 161, 413-421 (2005) · Zbl 1065.34076 · doi:10.1016/j.amc.2003.12.036
[20]Xu, S.; Lam, J.: Improved delay-dependent stability criteria for time-delay systems, IEEE trans. Autom. control 50, 384-387 (2005)
[21]Peng, C.; Tian, Y. -C.: Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay, J. comput. Appl. math. 214, 480-494 (2008) · Zbl 1136.93437 · doi:10.1016/j.cam.2007.03.009
[22]Kwon, O. M.; Park, J. H.; Lee, S. M.: On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays, Appl. math. Comput. 203, 843-853 (2008) · Zbl 1168.34046 · doi:10.1016/j.amc.2008.05.094
[23]Kwon, O. M.; Park, J. H.; Lee, S. M.: Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays, Appl. math. Comput. 207, 202-212 (2009) · Zbl 1178.34091 · doi:10.1016/j.amc.2008.10.018
[24]He, Y.; Wu, M.: Delay-dependent conditions for absolute stability of lurie control systems with time-varying delay, Acta autom. Sin. 31, 475-478 (2005)
[25]Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994)
[26]Kolmanovskii, V. B.; Myshkis, A.: Applied theory of functional differential equation, (1992)
[27]Nian, X. H.: Delay dependent conditions for absolute stability of lurie type control systems, Acta autom. Sin. 25, 564-566 (1999)
[28]Yang, B.; Wang, J. C.: Delay-dependent criterion for absolute stability of general neutral lurie systems, Acta autom. Sin. 30, 261-264 (2004)
[29]Gao, J. F.; Su, H. Y.; Ji, X. F.; Chu, J.: Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity, Nonlinear anal. Real world appl. 9, 2350-2360 (2008) · Zbl 1156.34345 · doi:10.1016/j.nonrwa.2007.07.003
[30]Park, J.: Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations, Appl. math. Comput. 161, 413-421 (2005) · Zbl 1065.34076 · doi:10.1016/j.amc.2003.12.036