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)
Establishing stability and instability of matrix hypercubes. (English) Zbl 1129.93467
Summary: The problem of establishing stability and instability of a matrix hypercube is considered and some conditions are proposed based on the stability boundary crossing principle and sum of squares relaxations. Specifically, a sufficient and asymptotically necessary condition for the stability is derived which can be checked through convex LMI optimizations. With respect to existing approaches that provide nonconservative conditions, the contribution consists of a significantly smaller computational burden in some cases. Indeed, even among small systems there are cases in which such approaches cannot be used due to the huge computational burden while the proposed technique can be easily applied. Moreover, a sufficient and asymptotically necessary condition for the instability is proposed which amounts to solving a linear algebra problem once that the condition for the stability has been investigated. Such a condition has never been proposed in the literature.
MSC:
93D05Lyapunov and other classical stabilities of control systems
34D20Stability of ODE