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)
Stochastic input-to-state stability and applications to global feedback stabilization. (English) Zbl 0953.93073
The author considers the stochastic composite system described by the following stochastic differential Ito equations $$\Sigma_1 :dx =f_1 (x,u)dt+ g_1(x,u) dw(t)$$ $$\Sigma_2: dy=f_2 (x,y,u)dt +g_2(x,y,u) dw(t)$$ where $(x,y) \in\bbfR^n \times\bbfR^k$ are the vectors of state, $u\in \bbfR^m$ is the control (input) vector, $f_i,g_i, i=1,2$ are nonlinear vector functions of appropriate dimensions and $w\in\bbfR$ is a standard Wiener process. The author introduces new definitions of stochastic $\gamma$-input to state stability and derives sufficient conditions for global stabilization in two cases, i.e., by means of output (linear and bounded) static feedback and by a dynamic feedback controller.

93E15Stochastic stability
93D15Stabilization of systems by feedback
93D25Input-output approaches to stability of control systems
93A15Large scale systems
Full Text: DOI