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)
Robust exact differentiation via sliding mode technique. (English) Zbl 0915.93013
Author’s summary: The main problem in differentiator design is to combine differentiation exactness with robustness with respect to possible measurement errors and input noises. The proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal. Such an order of the differential error is shown to be the best possible one when the only information known on the base signal is an upper bound for Lipschitz’s constant of the derivative.

93B12Variable structure systems
93B35Sensitivity (robustness) of control systems
93A30Mathematical modelling of systems
94A12Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI
[1] Carlsson, B.; Ahlen, A.; Sternad, M.: Optimal differentiation based on stochastic signal models. IEEE trans. Signal process 39, No. 2, 341-353 (1991) · Zbl 0728.93003
[2] Emelyanov, S. V.; Korovin, S. K.; Levantovsky, L. V.: Higher order sliding modes in the binary control systems. Sov. phys. Dokl. 31, No. 4, 291-293 (1986)
[3] Fillippov, A. F.: Differential equations with discontinuous right-hand slide. (1988)
[4] Fridman, L.; Levant, A.: Sliding modes of higher order as a natural phenomenon in control theory. Robust control via variable structure & Lyapunov techniques 217, 107-133 (1996) · Zbl 0854.93021
[5] Golembo, B. Z.; Emelyanov, S. V.; Utkin, V. I.; Shubladze, A. M.: Application of piecewise-continuous dynamic systems to filtering problems. Automat. remote control 37, No. 3, 369-377 (1976)
[6] Kumar, B.; Roy, S. C. D.: Design of digital differentiators for low frequencies. Proc. IEEE 76, 287-289 (1988)
[7] (Levantovsky, A. Levant; ), L. V.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58, No. 6, 1247-1263 (1993) · Zbl 0789.93063
[8] Levantovsky, L. V.: Second order sliding algorithmstheir realization. Dynamics of heterogeneous systems, 32-43 (1985)
[9] Luenberger, D. G.: An introduction to observers. IEEE trans. Automat. control, No. 16, 596-602 (1971)
[10] Nicosia, S.; Tornambe, A.; Valigi, P.: A solution to the generalized problem of nonlinear map inversion. Systems control lett 17, 383-394 (1991) · Zbl 0749.93059
[11] Pei, S. -C.; Shyu, J. -J.: Design of FIR Hilbert transformers and differentiators by eigenfilter. IEEE trans. Acoust. speech signal process, No. 37, 505-511 (1989)
[12] Rabiner, L. R.; Steiglitz, K.: The design of wide-band recursive and nonrecursive digital differentiators. IEEE trans. Audio electroacoust, No. 18, 204-209 (1970)
[13] Slotine, J. -J.E.; Hedrick, J. K.; Misawa, E. A.: On sliding observers for nonlinear systems. J. dyn. Systems measurement control 109, No. 9, 245-252 (1987) · Zbl 0661.93011
[14] Utkin, V. I.: Sliding modes in optimization and control problems. (1992) · Zbl 0748.93044