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)
Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. (English) Zbl 1228.93091
Summary: We consider the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov-Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.
MSC:
93D09Robust stability of control systems
34K20Stability theory of functional-differential equations
References:
[1]Slemrod, M.; Infante, E. F.: Asymptotic stability criteria for linear systems of differential equations of neutral type and their discrete analogues, J. math. Anal. appl. 38, 399-415 (1972) · Zbl 0202.10301 · doi:10.1016/0022-247X(72)90098-4
[2]Wu, H.; Liao, X.; Feng, W.; Guo, S.; Zhang, W.: Robust stability analysis of uncertain systems with two additive time-varying delay components, Appl. math. Modell. 33, 4345-4353 (2009) · Zbl 1173.93024 · doi:10.1016/j.apm.2009.03.008
[3]Li, X. G.; Zhu, X. -J.: Stability analysis of neutral systems with distributed delays, Automatica 44, 2197-2201 (2008)
[4]Zhang, D.; Yu, L.: H filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations, J. franklin inst. 347, 1374-1390 (2010) · Zbl 1202.93047 · doi:10.1016/j.jfranklin.2010.05.001
[5]Kwon, O. M.; Park, J. H.; Lee, S. M.: An improved delay-dependent criterion for asymptotic stability of uncertain dynamic systems with time-varying delays, J. optim. Theory appl. 145, 343-353 (2010) · Zbl 1201.93107 · doi:10.1007/s10957-009-9637-x
[6]Han, Q. L.: Robust stability of uncertain delay-differential systems of neutral type, Automatica 38, 719-723 (2002) · Zbl 1020.93016 · doi:10.1016/S0005-1098(01)00250-3
[7]Liu, X. G.; Wu, M.; Martin, R.; Tang, M. L.: Delay-dependent stability analysis for uncertain neutral systems with time-varying delays, Math. comput. Simul. 75, 15-27 (2007) · Zbl 1128.34048 · doi:10.1016/j.matcom.2006.08.006
[8]Niamsup, P.; Mukdasai, K.; Phat, V. N.: Improved exponential stability for time-varying systems with nonlinear delayed perturbations, Appl. math. Comput. 204, 490-495 (2008) · Zbl 1168.34355 · doi:10.1016/j.amc.2008.07.022
[9]Kuang, Y.: Delay differential equations with applications in population dynamics, (1993) · Zbl 0777.34002
[10]Brayton, R. K.: Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type, Quart. appl. Math. 24, 215-224 (1996) · Zbl 0143.30701
[11]Niculescu, S. I.: Delay effects on stability: A robust control approach, (2001)
[12]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
[13]Qiu, F.; Cui, B.; Ji, Y.: A delay-dividing approach to stability of neutral system with mixed delays and nonlinear perturbations, Appl. math. Modell. 34, 3701-3707 (2010) · Zbl 1201.93098 · doi:10.1016/j.apm.2010.03.013
[14]Kwon, O. M.; Park, J. H.; Lee, S. M.: On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays, Appl. math. Comput. 197, 864-873 (2008) · Zbl 1144.34052 · doi:10.1016/j.amc.2007.08.048
[15]Lien, C. H.; Yu, K. W.; Hsieh, J. G.: Stability conditions for a class of neutral systems with multiple delays, J. math. Anal. appl. 245, 20-27 (2000) · Zbl 0973.34066 · doi:10.1006/jmaa.2000.6716
[16]Chen, J. D.; Lien, C. H.; Fan, K. K.; Chou, J. H.: Criteria for asymptotic stability of a class of neutral systems via a LMI approach, IEE proc. Control theory appl. 148, 442-447 (2001)
[17]Fridman, E.: New Lyapunov – Krasovskiĭ functionals for stability of linear retarded and neutral type systems, Syst. control lett. 43, 309-319 (2001) · Zbl 0974.93028 · doi:10.1016/S0167-6911(01)00114-1
[18]Park, J. H.; Won, S.: Stability of neutral delay-differential systems with nonlinear perturbations, Int. J. Syst. sci. 31, 961-967 (2000) · Zbl 1080.93598 · doi:10.1080/002077200412113
[19]Yue, D.; Fang, J.; Won, S.: Delay-dependent exponential stability of a class of neutral systems with time delay and time-varying parameter uncertainties: an LMI approach, JSME int. J. ser. C 46, 245-251 (2003)
[20]Xiong, L.; Zhong, S.; Li, D.: Novel delay-dependent asymptotical stability of neutral systems with nonlinear perturbations, J. comput. Appl. math. 232, 505-513 (2009) · Zbl 1186.34102 · doi:10.1016/j.cam.2009.06.026
[21]Orihuela, L.; Millan, P.; Vivas, C.; Rubio, F. R.: Robust stability of nonlinear time-delay systems with interval time-varying delay, Int. J. Robust nonlin. Control 21, 709-724 (2011) · Zbl 1222.93173 · doi:10.1002/rnc.1616
[22]Kwon, O. M.; Park, J. H.; Lee, S. M.: On robust stability criterion for dynamic systems with time-varying delays and nonlinear perturbations, Appl. math. Comput. 203, 937-942 (2008) · Zbl 1168.34354 · doi:10.1016/j.amc.2008.05.097
[23]Cao, Y. -Y.; Lam, J.: Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations, Int. J. Syst. sci. 31, 359-365 (2000) · Zbl 1080.93519 · doi:10.1080/002077200291190
[24]Shen, C. C.; Zhong, S. M.: New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties, Chaos, solitons fractals 40, 2277-2285 (2009) · Zbl 1198.93164 · doi:10.1016/j.chaos.2007.10.020
[25]Yang, B.; Wang, J. C.; Pan, X. J.; Zhong, C. Q.: Delay-dependent criteria for robust stability of linear neutral systems with time-varying delay and nonlinear perturbations, Int. J. Syst. sci. 38, 511-518 (2007) · Zbl 1126.93046 · doi:10.1080/00207720701393302
[26]Zou, Z.; Wang, Y.: New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations, IEE proc. Control theory appl. 153, 623-626 (2006)
[27]Zhao, Z.; Wang, W.; Yang, B.: Delay and its time-derivative dependent robust stability of neutral control system, Appl. math. Comput. 187, 1326-1332 (2007) · Zbl 1114.93076 · doi:10.1016/j.amc.2006.09.042
[28]Han, Q. L.: On robust stability for a class of linear systems with time-varying delay and nonlinear perturbations, Comput. math. Appl. 47, 1201-1209 (2004) · Zbl 1154.93408 · doi:10.1016/S0898-1221(04)90114-9
[29]Han, Q. L.; Yu, L.: Robust stability of linear neutral systems with nonlinear parameter perturbations, IEE proc. Control theory appl. 151, 539-546 (2004)
[30]Zhang, W. A.; Yu, L.: Delay-dependent robust stability of neutral systems with mixed delays and nonlinear perturbations, Acta autom. Sin. 33, 863-866 (2007)
[31]Chen, Y.; Xue, A.; Lu, R.; Zhou, S.: On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations, Nonlinear anal.: theory, methods appl. 68, 2464-2470 (2008) · Zbl 1147.34352 · doi:10.1016/j.na.2007.01.070
[32]Zhang, J. H.; Peng, S.; Qiu, J. Q.: Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties, Chaos, solitons fractals 38, 160-167 (2008) · Zbl 1142.93402 · doi:10.1016/j.chaos.2006.10.068
[33]Qiu, F.; Cui, B.; Ji, Y.: Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations, Nonlinear anal.: real world appl. 11, 895-906 (2010) · Zbl 1187.37124 · doi:10.1016/j.nonrwa.2009.01.032
[34]Rakkiyappan, R.; Balasubramaniam, P.; Krishnasamy, R.: Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations, J. comput. Appl. math. 235, 2147-2156 (2010) · Zbl 1211.34087 · doi:10.1016/j.cam.2010.10.011
[35]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
[36]Sun, J.; Liu, G. P.; Chen, J.: Delay-dependent stability and stabilization of neutral time-delay systems, Int. J. Robust nonlinear control 19, 1364-1375 (2009) · Zbl 1169.93399 · doi:10.1002/rnc.1384
[37]Sun, J.; Liu, G. P.: A new delay-dependent stability criterion for time-delay systems, Asian J. Control 11, 427-431 (2009)