Stability and Robust Stability  of Linear Time-Invariant Delay Differential-Algebraic Equations

Du, Nguyen Huu; Linh, Vu Hoang; Mehrmann, Volker; Thuan, Do Duc

doi:10.1137/130926110

Cited by 41 publications

(35 citation statements)

References 33 publications

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“…These results, which are presented in details in [18,Section 4], extend previous results on DODEs and DAEs in [7,8,17,19,36,55]. Suppose that system (19.1) is exponentially stable and consider a perturbed system (19.28) where i 2 C p i ;q , i D 1; 2; 3 are perturbations and B i 2 C n;p i , i D 1; 2; 3, C 2 C q;n , are matrices that restrict the structure of the perturbations.…”

Section: Stability Radiimentioning

confidence: 77%

“…For an illustration of the results, see [18,Example 4.14]. Finally, we note that a similar robust stability problem can be formulated for linear time-invariant DAEs with multiple delays subject to multiple/affine perturbations and a formula of the complex stability radius can be obtained analogously.…”

Section: Corollarymentioning

confidence: 92%

“…So, strangeness-free DDAEs generalizes index-1 regular DDAEs which have been discussed so far in the literature [13,20,45]. We refer to [18] for more details.…”

Section: Definitionmentioning

confidence: 95%

“…In practice, such a scaling matrix W and the corresponding transformed coefficient matrices can be easily constructed by using the singular value decomposition (SVD) of matrices, see the detailed procedure in [18]. Following the concept of strangeness-index in [37] we make the following definition, see also [25].…”

Section: Preliminary Notions and Transformationsmentioning

confidence: 99%

“…Proposition 3.4 in [18] shows that the allowable delay conditions ND 21 D 0 and ND 22 D 0 are simultaneously satisfied if and only if We note that although the spectral criterion˛.H / < 0 was used for characterizing the exponential stability of DDAEs with regular pair .E; A/ of arbitrary index in [13,63,67], a rigorous proof had not been available prior to the appearance [18].…”

Section: Spectrum-based Stability Analysismentioning

confidence: 99%

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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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Section: Stability Radiimentioning

confidence: 77%

Section: Corollarymentioning

confidence: 92%

“…So, strangeness-free DDAEs generalizes index-1 regular DDAEs which have been discussed so far in the literature [13,20,45]. We refer to [18] for more details.…”

Section: Definitionmentioning

confidence: 95%

Section: Preliminary Notions and Transformationsmentioning

confidence: 99%