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)
Real analytic geometry and local observability. (English) Zbl 0968.93015
Ferreyra, G. (ed.) et al., Differential geometry and control. Proceedings of the Summer Research Institute, Boulder, CO, USA, June 29-July 19, 1997. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 64, 65-72 (1999).
From the author’s abstract: “The language of real analytic geometry is used to give necessary and sufficient conditions of stable local observability of analytic systems… Globalization of this result yields a new characterization of local observability at large which uses the concept of sheaf.” The notion of indistinguishability and theorem 3.1 giving necessary and sufficient conditions for this property are the basic material of the paper. Theorem 3.1 is taken from a paper of other authors [{\it R. Hermann} and {\it A. Krener}, Nonlinear controllability and observability, IEEE Trans. Autom. Control AC-22, 728-740 (1977; Zbl 0396.93015)] without proof. The definition of an algebra ${\cal H}$ of real analytic functions by means of which the conditions above are expressed makes the reviewer have his doubts about the correctness of the theorem: the definition of indistinguishability also contains some conditions concerning the control parameter; conclusions resulting from the corresponding partial derivatives seem to have been forgotten. In the fourth chapter (“Globalization”) the author “uses the concept of sheaf” in the following way. “H is identified with the set of sections of the sheaf $x\to{\cal H}_x$…” Obviously he has not become aware of the problem of completeness of the presheaf ${\cal H}$. For the entire collection see [Zbl 0903.00046].
93B27Geometric methods in systems theory
14P15Real analytic and semianalytic sets
93B29Differential-geometric methods in systems theory (MSC2000)