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)
Lower bounds on the solution of coupled algebraic Riccati equation. (English) Zbl 0990.93043
Lower bounds for eigenvalues and lower matrix bounds of the solution to a continuous-time coupled algebraic Riccati equation (CCARE) and a discrete-time coupled algebraic Riccati equation (DCARE) are developed. These bounds are obtained as special cases of bounds for the unified coupled algebraic Riccati equation. They include bounds for the minimal eigenvalues, the sums of the eigenvalues, the trace and the determinant. Two low-order numerical examples are presented. The examples suggest that the bounds for CCARE can be very conservative, the bounds for DCARE being quite satisfactory.
93B60Eigenvalue problems in systems theory
49N10Linear-quadratic optimal control problems
15A24Matrix equations and identities
15A45Miscellaneous inequalities involving matrices
15A15Determinants, permanents, other special matrix functions