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)
Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays. (English) Zbl 1152.93404
Summary: We investigate the adaptive output-feedback stabilisation for a class of stochastic non-linear systems with time-varying time delays. First, we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non-linear systems with time delays, and introduce a new stability notion and the related criterion. Then, for a class of stochastic non-linear systems with time-varying time delays, uncertain parameters in both drift and diffusion terms, and general constant virtual control coefficients, we present a systematic design procedure for a memoryless adaptive output-feedback control law by using the backstepping method. It is shown that under the control law based on a memoryless observer, the closed-loop equilibrium of interest is globally stable in probability, and moreover, the solution process can be regulated to the origin almost surely.

93C40Adaptive control systems
93D15Stabilization of systems by feedback
Full Text: DOI