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)
Stabilization of uncertain systems via linear control. (English) Zbl 0554.93054

The paper gives two elementary results on the feedback stability of time- varying systems defined by x ˙=A(q)x+B(q)u, where q is a time- varying parameter. (i) The stability of the system with a linear feedback u=Kx can be decided by a quadratic Lyapunov function if and only if the same is true of the system

y ˙=A0B0y+0Iu;

(ii) If with u=p(x), where p(0)=0 and p is continuously differentiable, the feedback system has a quadratic Lyapunov function, then with u=(p/x) x=0 x it also has a quadratic Lyapunov function.

Reviewer: S.Mossaheb

93D15Stabilization of systems by feedback
93C99Control systems, guided systems
93D05Lyapunov and other classical stabilities of control systems
93C05Linear control systems
93D20Asymptotic stability of control systems
34D20Stability of ODE