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)
Robust stabilization of a class of polytopic linear time-varying continuous systems under point delays and saturating controls. (English) Zbl 1143.93021
Summary: This paper investigates the stabilization dependent on the delays of, in general, time-varying linear systems with multiple constant point time-delays under saturating state-feedback controls. The matrices describing the state-space dynamics and control belong to polytopes. Also, the controller gain matrix is characterized as belonging to another polytope whose vertices are computed from the knowledge of a closed bounded ball containing a set of values of the state norm and also the component-wise saturating gains and saturation parameterizations. This knowledge defines the polytope vertices through scaling diagonal matrices being associated with the various operation modes in the linear and saturated zones of each input component. In these conditions, the resulting closed-loop system is of polytopic nature whose whole number of vertices is (at most) equal to the product of both numbers of vertices of the above two polytopes characterizing the plant parameterization and the saturation. The closed-loop sufficiency-type stability conditions are obtained from Lyapunov’s stability theory by constructing candidates for each vertex of the polytopic closed-loop system each satisfying, in the most general case, a Riccati matrix differential inequality. Some conditions guaranteeing the stability conditions are obtained from a general Kalman-Yakubovtch-Popov (KYP) Lemma and some weaker stability conditions are also obtained for the time-invariant case from a set of linear matrix inequalities associated with the set of vertices.
MSC:
93D09Robust stability of control systems
93C10Nonlinear control systems
93C15Control systems governed by ODE