# 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 calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators. (English) Zbl 0632.34005
A link is established between the definition of Filippov’s solution concept for ordinary differential equations with a discontinuous right- hand side [{\it A. F. Filippov}, Mat. Sb., N. Ser. 51(93), 99-128 (1960; Zbl 0138.322)] and Clarke’s generalized gradient [{\it F. H. Clarke}, Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]. According to Filippov’s definition, solutions to $\dot x=f(x)$ are those to the differential inclusion $\dot x(t)\in K(f)(x(t))$, where K(f) is a suitably defined multifunction depending on f. The authors remark that if f is locally Lipschitz, then $K(\nabla f)=\partial f$, where $\partial f$ denotes Clarke’s generalized gradient. This relation is useful for computing K in various situations. Such a calculus is applied to the variable structure control of a robot manipulator.
Reviewer: T.Zolezzi

##### MSC:
 34A34 Nonlinear ODE and systems, general
Full Text: