Maß- und Integrationstheorie

Elstrodt, Jürgen

doi:10.1007/978-3-662-08527-1

Cited by 52 publications

(49 citation statements)

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“…Di erent values v + = v − , -+ = -− are obtained as soon as t belongs to the discontinuity points {t i }. For a thorough treatment of bounded variation functions, absolute continuity and measures we refer in particular to Reference [13], or to any advanced text book on integration theory, such as Reference [14] or Reference [15].…”

Section: Models Of Switches In Electrical Systemsmentioning

confidence: 99%

“…By a closer look at Figures 13,14 and Equations (44), we see that the circuit is composed of three fundamental loops with di erent properties: In terms of mechanics, loop 1 corresponds to a static subsystem and is described by an algebraic equation according to the ÿrst equilibrium of measures in Equation (44). Loop 2 corresponds to a dynamic subsystem and is described by a second order measure equality with possible impulsive behaviour, as seen from the second equation in Equation (44).…”

Section: The Original Dc-dc Buck Convertermentioning

confidence: 99%

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Models of non-smooth switches in electrical systems

Glocker

2005

Int. J. Circ. Theor. Appl.

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SUMMARYIdealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of set-valued functions, which allow to formulate the circuit's dynamic behaviour as a di erential inclusion. This approach is demonstrated by the example of the DC-DC buck converter. A di erence scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the set-valued branch relations in order to obtain a minimal model, is performed on the example of the buck converter.

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Section: Models Of Switches In Electrical Systemsmentioning

confidence: 99%

Section: The Original Dc-dc Buck Convertermentioning

confidence: 99%

Models of non-smooth switches in electrical systems

Glocker

2005

Int. J. Circ. Theor. Appl.

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“…a set such that for each uncountable closed set C we have C ∩ T = ∅ and C ∩ T = ∅ (see for instance the proof of Theorem 3.10 pp. 101-102 of [1]). Now we obtain…”

Section: Example 211mentioning

confidence: 99%

Pointwise measurable functions

Render¹,

Rogge²

2004

MATH. SCAND.

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We introduce the new concept of pointwise measurability. It is shown in this paper that a measurable function is measurable at each point and that for a large class of topological spaces the converse also holds. Moreover it can be seen that a function which is continuous at a point is Borel-measurable at this point too. Furthermore the set of measurability points is considered. If the range space is a σ -compact metric space, then this set is a G δ -set; if the range space is only a Polish space this is in general not true any longer.

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“…Consequently, their effective domains dom (f qc ) and dom (f (qc) ) are measurable subsets of R nm (cf. [21], p. 105, Thm. 4.2), and the restrictions f qc dom (f qc ) and f (qc) dom (f (qc) ) are measurable functions.…”

Section: Theorem 218 (Properties Of Fmentioning

confidence: 99%

On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)

Wagner

2009

ESAIM: COCV

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Abstract.Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K ⊂ R nm instead of the whole space R nm as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous quasiconvex envelopeOur main result is a representation theorem for f (qc) which generalizes Dacorogna's well-known theorem on the representation of the quasiconvex envelope of a finite function. The paper will be completed by the calculation of f (qc) in two examples.Mathematics Subject Classification. 26B25, 26B40, 49J45, 52A20.

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Maß- und Integrationstheorie

Cited by 52 publications

References 0 publications

Models of non-smooth switches in electrical systems

Models of non-smooth switches in electrical systems

Pointwise measurable functions

On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)

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