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)
A converse Lyapunov theorem for nonuniform in time global asymptotic stability and its application to feedback stabilization. (English) Zbl 1049.93073

The paper studies the notion of nonuniform in time robust global asymptotic stability (RGAS) for time-varying, nonlinear systems of the general form

x ˙=f(t,x,d),x n ,dD,t0

where D is a compact subset of m . The authors present some equivalent definitions of RGAS and provide a Lyapunov characterization. These results are applied to derive necessary and sufficient conditions for ISS-feedback stabilization of input time-varying, nonlinear systems: this actually constitutes an extension of the well-known Artstein-Sontag theorem. For systems which exhibit an affine structure, an explicit formula of the stabilizing feedback is given. Finally, ISS-stabilization is also considered for certain cascade systems.


MSC:
93D20Asymptotic stability of control systems
93D30Scalar and vector Lyapunov functions
37B55Nonautonomous dynamical systems
93D15Stabilization of systems by feedback
93D25Input-output approaches to stability of control systems