Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions

Campbell, Stephen L.; Linh, Vu Hoang

doi:10.1016/j.amc.2008.12.008

Cited by 39 publications

(43 citation statements)

References 18 publications

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“…Of course, DDAEs inherit all the difficulties that are associated with both DAEs and DDEs. Their interaction, however, leads to new effects that do not arise in either DAEs or DDEs, as has been pointed out in [2,6,8].…”

Section: P Ha and V Mehrmannmentioning

confidence: 99%

“…[4,12,13], the theoretical understanding and the development of appropriate numerical methods for DDAEs, however, is far from complete even for the case of linear systems with constant coefficients. Only very few results are available, see e.g., [1,2,6,7,8,19], and these are mainly for the special case of DAEs, where the delay component is nothing else than an additional part of the inhomogeneity.…”

Section: P Ha and V Mehrmannmentioning

confidence: 99%

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Analysis and reformulation of linear delay differential-algebraic equations

Ha¹,

Mehrmann²

2012

ELA

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Abstract. General linear systems of delay differential-algebraic equations (DDAEs) of arbitrary order are studied in this paper. Under some consistency conditions, it is shown that every linear highorder DAE can be reformulated as an underlying high-order ordinary differential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay differential equation (DDE). Condensed forms for DDAEs based on the algebraic structure of the system coefficients are derived and these forms are used to reformulate DDAEs as strangeness-free systems, where all constraints are explicitly available. The condensed forms are also used to investigate structural properties of the system like solvability, regularity, consistency and smoothness requirements.

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Section: P Ha and V Mehrmannmentioning

confidence: 99%

Section: P Ha and V Mehrmannmentioning

confidence: 99%

Analysis and reformulation of linear delay differential-algebraic equations

Ha¹,

Mehrmann²

2012

ELA

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“…However, by introducing a new variable, (19.3) can be rewritten into the form (19.1) with double dimension, see [13]. For this reason here we only consider (19.1).…”

Section: Introductionmentioning

confidence: 97%

“…Many of the results that are known for DODEs cannot be extended to the DDAE case. Even the well-known spectral analysis for the exponential stability or the asymptotic stability of linear timeinvariant DDAEs (19.1) is much more complex than that for DAEs and DDEs, see [13,63,67] for some special cases.…”

Section: Introductionmentioning

confidence: 99%

Spectrum-Based Robust Stability Analysis of Linear Delay Differential-Algebraic Equations

Linh

Thuan

2015

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

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This paper presents a survey of results on the spectrum-based robust stability analysis of linear delay ordinary differential equations (DODEs) and linear delay differential-algebraic equations (DDAEs). We focus on the formulation of stability radii for continuous-time delay systems with coefficients subject to structured perturbations. First, we briefly overview important results on the stability radii for linear time-invariant DODEs and an extended result for linear time-varying DODEs. Then, we survey some recent results on the spectrum-based stability and robust stability analysis for general linear time-invariant DDAEs. IntroductionThis paper is concerned with the robust stability of homogeneous linear timeinvariant delay systems of the formwhere E; A; D 2 K n;n , K D R or K D C, and > 0 represents a time-delay. We study initial value problems with an initial function , so that x.t/ D .t/; for Ä t Ä 0: (19.2)

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“…Due to these reasons, recently more and more attention has been devoted to DDAEs, [3][4][5][6][7][8][9]. One of the most important research topics in the qualitative theory of DDAE systems is the stability analysis, which has attracted many researches in recent years, [2,[5][6][7]10]. It is well known, that for DDEs of the form (3), stability properties of the solution are closely related to spectral conditions of the matrix triple (I, A, B) , see [11].…”

Section: Introduction0 F *mentioning

confidence: 99%

On the Stability Analysis of Delay Differential-Algebraic Equations

Ha¹

2018

MaP

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Abstract:The stability analysis of linear time invariant delay differential-algebraic equations (DDAEs) is analyzed. Examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical systems is not valid for an arbitrarily high index system, and hence, a new concept of weak exponential stability (w.e.s) is proposed. Then, we characterize the w.e.s in term of a spectral condition for some special classes of DDAEs.

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Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions

Cited by 39 publications

References 18 publications

Analysis and reformulation of linear delay differential-algebraic equations

Analysis and reformulation of linear delay differential-algebraic equations

Spectrum-Based Robust Stability Analysis of Linear Delay Differential-Algebraic Equations

On the Stability Analysis of Delay Differential-Algebraic Equations

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