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)
LMI-based computation of optimal quadratic Lyapunov functions for odd polynomial systems. (English) Zbl 1056.93059
Summary: The problem of estimating the domain of attraction (DA) of equilibria is considered for odd polynomial systems. Specifically, the computation of the optimal quadratic Lyapunov function (OQLF), i.e. the quadratic Lyapunov function (QLF) which maximizes the volume of the largest estimate of the DA (LEDA), is addressed. In order to tackle this double non-convex optimization problem, a relaxation approach based on homogeneous polynomial forms is proposed. The first contribution of the paper shows that a lower bound of the LEDA for a fixed QLF can be obtained via linear matrix inequalities (LMIs) based procedures. Also, condition for checking tightness of the lower bound are provided. The second contribution is a strategy for selecting a good starting point for the OQLF search, which is based on the volume maximization of the region where the time derivative of the QLFs is negative and is given in terms of LMIs. Several application examples are presented to illustrate the numerical behaviour of the proposed approach.
93D30Scalar and vector Lyapunov functions
93B40Computational methods in systems theory