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)
Numerically robust delta-domain solutions to discrete-time Lyapunov equations. (English) Zbl 1106.65314
Summary: A problem of numerical conditioning of a special kind of discrete-time Lyapunov equations is considered. It is assumed that a discretization procedure equipped with the zero-order holder mechanism is utilized that leads to the data matrices that are affinely related to the sampling period and matrices that are independent or linearly related to the squared sampling period. It is shown that common forward shift operator techniques for solving these equations become ill-conditioned for a sufficiently small sampling period and that numerical robustness and reliability of computations can be significantly improved via utilizing the so-called delta operator form of the origin equations.
MSC:
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
93B40Computational methods in systems theory
93C55Discrete-time control systems
Software:
mctoolbox; LAPACK