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-range-dependent control synthesis for time-delay systems with actuator saturation. (English) Zbl 1155.93350
Summary: The control synthesis problem for a class of linear time-delay systems with actuator saturation is investigated in this paper. The time delay is considered to be time-varying and has lower and upper bounds. A delay-range-dependent approach is adopted and the corresponding existence conditions of the stabilizing state-feedback controller are derived in terms of LMIs. An estimate for the domain of attraction of the origin can be obtained for the underlying systems with different time-delay ranges. Two numerical examples are presented to show the effectiveness and less conservatism of the developed theoretical results.

MSC:
 93B50 Synthesis problems 93B52 Feedback control
Full Text:
References:
 [1] Boukas, E. K.; Liu, Z. K.: Deterministic and stochastic time-delay systems, (2002) · Zbl 1056.93001 [2] Cao, Y. Y.; Z., L.; Hu, T.: Stability analysis of linear time-delay systems subject to input saturation, IEEE transactions on circuits and systems (II) 49, No. 2, 233-240 (2002) [3] Fridman, E.; Pila, A.; Shaked, U.: Regional stabilization and H$\infty$control of time-delay systems with saturating actuators, International journal of robust & nonlinear control 13, No. 9, 885-907 (2003) · Zbl 1029.93022 · doi:10.1002/rnc.852 [4] Gao, H.; Lam, J.; Wang, C.; Wang, Y.: Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay, IET control theory & applications 151, No. 6, 691-698 (2004) [5] He, Y.; Wang, Q. G.; Lin, C.; Wu, M.: Delay-range-dependent stability for systems with time-varying delay, Automatica 43, No. 2, 371-376 (2007) · Zbl 1111.93073 · doi:10.1016/j.automatica.2006.08.015 [6] Hu, T.; Lin, Z.; Chen, B. M.: An analysis and design method for linear systems subject to actuator saturation and disturbance, Automatica 38, No. 2, 351-359 (2002) · Zbl 0991.93044 · doi:10.1016/S0005-1098(01)00209-6 [7] Jiang, X.; Han, Q. L.: On H$\infty$control for linear systems with interval time-varying delay, Automatica 41, No. 12, 2099-2106 (2005) · Zbl 1100.93017 · doi:10.1016/j.automatica.2005.06.012 [8] Kharitonov, V. L.; Niculescu, S. I.: On the stability of linear systems with uncertain delay, IEEE transactions on automatic control 48, No. 1, 127-132 (2003) [9] Park, P.: A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE transactions on automatic control 44, No. 4, 876-877 (1999) · Zbl 0957.34069 · doi:10.1109/9.754838 [10] Said, O.: Synthesis of controllers for time-delay systems subject to actuator saturation and disturbance, Journal of dynamic systems, measurement, and control 125, No. 2, 244-249 (2003) [11] Tarbourieh, S.; Gomes, J. M.: Synthesis of controllers for continuous-time delay systems with saturating controls via LMI, IEEE transactions on automatic control 45, No. 1, 105-111 (2000) · Zbl 0978.93062 · doi:10.1109/9.827364 [12] Wu, M.; He, Y.; She, J. H.; Liu, G. P.: Delay-dependent criteria for robust stability of time-varying delay systems, Automatica 40, No. 8, 1435-1439 (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004 [13] Zhang, L., Boukas, E., & Haidar, A. (2007). Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Technical report, Ecole Polytechnique de Montreal · Zbl 1155.93350 [14] Zhang, L.; Shi, P.; Boukas, E.: H$\infty$output-feedback control for switched linear discrete-time systems with time-varying delays, International journal of control 80, No. 8, 1354-1365 (2007) · Zbl 1133.93316 · doi:10.1080/00207170701377113 [15] Zhang, L.; Shi, P.; Boukas, E.; Wang, C.: Robust l2-l$\infty$filtering for switched linear discrete time-delay systems with polytopic uncertainties, IET control theory & applications 1, No. 3, 722-730 (2007)