# 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)
Delay-dependent robust stability of uncertain nonlinear systems with time delay. (English) Zbl 1060.34041
The paper deals with the stability of uncertain delay differential equations. Using the Lyapunov method a new delay-dependent stability criterion is obtained.

##### MSC:
 34K20 Stability theory of functional-differential equations
Full Text:
##### References:
 [1] Yan, J. J.: Robust stability analysis of uncertain time delay systems with delay-dependence. Electron. lett. 37, No. 2, 135-137 (2001) [2] Yan, J. J.; Tsai, J. S. H.; Kung, F. C.: A new result on the robust stability of uncertain systems with time-varying delay. IEEE trans. Circ. syst.-I 48, No. 7, 914-916 (2001) · Zbl 1003.93037 [3] Doyle, J. C.; Glover, K.; Khargonekar, P. P.; Francis, B. A.: State-space solution to standard H2 and H$\infty$control problems. IEEE trans. Autom. contr. 34, 831-846 (1989) · Zbl 0698.93031 [4] Liu, P. L.; Su, T. J.: Robust stability of interval time-delay systems with delay-dependence. Syst. contr. Lett. 33, 231-239 (1998) · Zbl 0902.93052 [5] Su, J. H.: Further results on the robust stability of linear systems with a single delay. Syst. contr. Lett. 23, 374-379 (1994) · Zbl 0805.93045 [6] Trinh, H.; Aldeen, M.: Stability robustness bound for linear systems with delayed perturbations. IEEE proc. D contr. Theory appl. 142, 345-350 (1995) · Zbl 0831.93050 [7] Wu, H.; Mizukami, K.: Robust stability criteria for dynamical systems in delayed perturbations. IEEE trans. Autom. contr. 40, 487-490 (1995) · Zbl 0821.93060 [8] Hamed, A.: On the stability of time delay systems: new result. Int. J. Contr. 43, 321-324 (1986) [9] Mori, T.; Noldus, E.; Kuwahara, M.: A way to stabilize linear systems with delayed state. Automatica 19, 571-573 (1983) · Zbl 0544.93055 [10] Xu, B.: Comments on robust stability of delay dependence for linear uncertain systems. IEEE trans. Autom. contr. 39, 2365 (1994) · Zbl 0825.93605 [11] Oucheriah, S.: Measure of robustness for uncertain time-delay linear system. ASME J. Dyn. syst. Meas. contr. 117, 633-635 (1995) · Zbl 0844.93063 [12] Kolmanovskii, V. B.; Niculescu, S.; Richard, J.: On the Lyapunov--Krasovskiĭ functionals for stability analysis of linear delay systems. Int. J. Contr. 72, No. 4, 374-384 (1999) · Zbl 0952.34057 [13] V.B. Kolmanovskii, S. Niculescu, K. Gu, Delay effects on stability: a survey, Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona, USA, December 1999, pp. 1993--1998 [14] Kim, Jin-Hoon: Delay and its time-derivative dependent robust stability of time delayed linear systems with uncertainty. IEEE trans. Autom. contr. 46, No. 5, 789-792 (2001) · Zbl 1008.93056