zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
A sliding mode control for linear fractional systems with input and state delays. (English) Zbl 1221.93048
Summary: A sliding mode control design for fractional order systems with input and state time-delay is proposed. First, we consider a fractional order system without delay for which a sliding surface is proposed based on fractional integration of the state. Then, a stabilizing switching controller is derived. Second, a fractional system with state delay is considered. Third, a strategy including a fractional state predictor input delay compensation is developed. The existence of the sliding mode and the stability of the proposed control design are discussed. Numerical examples are given to illustrate the theoretical developments.

93B12Variable structure systems
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
[1] Richard, J. -P.: Time delay systems: an overview of some recent advances and open problems, Automatica 39, 1667-1694 (2003) · Zbl 1145.93302 · doi:10.1016/S0005-1098(03)00167-5
[2] Qu S-C, Wang Y-J. Sliding mode control for a class of uncertain input-delay systems. In: Proceedings of the 5th world congress on intelligent control and automation, Hanghzou, PRChina; June 15 -- 19, 2004.
[3] Al-Shamali SA, Crisalle OD, Latchman HA. An approach to stabilize linear systems with state and input delay. In: Proceedings of the American control conference Denver, Colorado; June 4 -- 6, 2003.
[4] El-Khezali R, Ahmad WH. Variable structure control of fractional time-delay systems. In: Proceedings of the 2nd IFAC, Workshop on fractional differentiation and its applications, Porto, Portugal; July 19 -- 21, 2006.
[5] Utkin, V. I.: Variable structure systems with sliding mode, IEEE trans automat cont 26, No. 2, 212-222 (1977) · Zbl 0382.93036 · doi:10.1109/TAC.1977.1101446
[6] Xia Y, Han J, Jia Y. A sliding mode control for linear systems with input and state delays. In: Proceedings of the 41st IEEE conference on decision and control. Las Vegas, Nevada USA; December, 2002.
[7] Roh, Y. -H.; Oh, J. -H.: Sliding mode control for robust stabilization of uncertain input-delay systems, Icase 2, No. 2, 98-103 (2000)
[8] Roh, Y. -H.; Oh, J. -H.: Robust stabilization of uncertain input delay systems by sliding mode control with delay compensation, Automatica 35, 1861-1865 (1999) · Zbl 0931.93015 · doi:10.1016/S0005-1098(99)00106-5
[9] Li, X.; Yurkovich, S.: Sliding mode control of delayed systems with application to engine idle speed control, IEEE trans on cont syst techn 9, No. 6, 802-810 (2001)
[10] Fridman L, Acosta P, Polyakov A. Robust eigenvalue assignment for uncertain delay control systems. In: Proceedings of the 3rd IFAC international workshop on time delay systems, Santa Fe, New Mexico; December 8 -- 10, 2001.
[11] Vinagre BM, Feliu V. Modeling and control of dynamic systems using fractional calculus: Application to electrochemical processes and flexible structures. In: Proceedings of 41st IEEE conference on decision and control, Las Vegas; 2002.
[12] Magin, R. -L.: Fractional calculus in bioengineering, (2006)
[13] Matignon D. Stability result on fractional differential equations with applications to control processing. In: Proceedings conference of IMACS, IEEE-SMC, Lille, France; July 1996. p. 963 -- 8.
[14] Matignon D, D’Andréa-Novel B. Some results on controllability and observability on finite dimensional fractional differential systems. In: Proceedings conference of IMACS, IEEE-SMC, Lille, France, July 1996. p. 952 -- 6.
[15] Lin J. Modélisation et identification des systèmes d’ordre non entiers, Dissertation. France: University of Poitiers; 2001.
[16] Podlubny, I.: Fractional-order systems and PI$\lambda d\mu $ controllers, IEEE trans automat cont 44, No. 1, 208-214 (1999) · Zbl 1056.93542 · doi:10.1109/9.739144
[17] Oustaloup, A.: La commande CRONE. Commande robuste d’ordre non entier, (1991) · Zbl 0864.93003
[18] Calderon AJ, Vinagre BM, Feliu V. Fractional sliding mode control of a DC-DC buck converter with application to DC motor drives. In: Paper presented at the 11th international conference on advanced robotics. University of Coimbra, Portugal, June 30 -- July 3, 2003.
[19] Kilbas, A. -A.; Srivastava, H. -M.; Trujillo, J. -J.: Theory and applications of fractional differential equations, Mathematics studies 204 (2006) · Zbl 1092.45003
[20] Ahn H, Chen YQ, Podlubny I. Robust stability checking of a class of linear interval fractional order system using Lyapunov inequality. In: Proceedings of the 2nd IFAC, workshop on fractional differentiation and its applications, Porto, Portugal, July19 -- 21, 2006.
[21] Garcia G, Messaoud H, Maraoui S. Practical stabilisation of linear time-varying systems, Sixième conférence internationale des Sciences et des Techniques de l’Automatique- STA’2005, Sousse, Tunisie, 19 -- 21 décembre, 2005.
[22] Khalil, H. -K.: Nonlinear systems, (2002) · Zbl 1003.34002
[23] Artstein, Z.: Linear systems with delayed controls: A reduction, IEEE trans automat cont 27, No. 4, 869-879 (1982) · Zbl 0486.93011 · doi:10.1109/TAC.1982.1103023
[24] Kwon, W. H.; Pearson, A. E.: Feedback stabilization of linear systems with delayed control, IEEE trans automat cont 25, No. 2, 266-269 (1980) · Zbl 0438.93055 · doi:10.1109/TAC.1980.1102288