Differential-Algebraic Equations: A Projector Based Analysis

Lamour, René; März, Roswitha; Tischendorf, Caren

doi:10.1007/978-3-642-27555-5

Cited by 221 publications

(280 citation statements)

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“…Given two matrices A, B in W ixn the matrix pencil {A,B} is defined as the one-parameter family XA + B [22,27,28,29,30]. If the polynomial (in A) det(XA + B) does not vanish identically (that is, if there exists at least one value of A for which det(AA + B) ^ 0), the matrix pencil is called regular.…”

Section: Discussionmentioning

confidence: 99%

“…is called a semiexplicit differential-algebraic equation (DAE) [22,27,28,29]. It is said to be index one if the matrix g y of partial derivatives of g with respect to the variables y is non-singular.…”

Section: Discussionmentioning

confidence: 99%

“…the Appendix and [22,27,28,29]), as an indexone characterization of second order mem-circuits. We will exploit this point of view later in Section 5.…”

Section: <"Mi Vw 1 Vji) I-uc-mentioning

confidence: 99%

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Second order mem‐circuits

Riaza

2014

Circuit Theory & Apps

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This paper presents a comprehensive taxonomy of so-called second order memory devices, which include charge-controlled memcapacitors and flux-controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second order mem-circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard we explore certain bifurcation phenomena exhibited by a family of circuits including a charge-controlled memcapacitor and a flux-controlled meminductor, providing some directions for future research.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Second order mem‐circuits

Riaza

2014

Circuit Theory & Apps

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“…These include the differentiation, geometric, perturbation, strangeness and tractability indices; cf. [8,29,40,39,54,59]. All these concepts generalize the notion of the nilpotency index of a matrix pencil, and support different approaches to the analysis and the numerical simulation of DAEs.…”

Section: The Index Of a Daementioning

confidence: 92%

“…to the non-degeneracy of the circuit, the state formulation problem or different qualitative issues [15,24,31,65]. The reader is referred to [8,29,40,39,54,59] for detailed introductions to the different index notions in DAE theory.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Analysis of Nonlinear Circuits: DAE Models with Indices Zero and One

Vega

Riaza

2013

Circuits Syst Signal Process

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We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest-structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers and other multiterminal devices.

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