Growth bound of delay-differential algebraic equations

Boisgérault, Sébastien

doi:10.1016/j.crma.2013.08.001

Cited by 2 publications

(5 citation statements)

References 11 publications

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“…There exists η > 0 such that any connected component Λ of the set Z η is bounded and such that Λ ⊂ P σ− if Λ ∩ P σ = ∅. Moreover, there exists κ > 0 such that |det(F )| ≥ κ on P σ− \Z η Proof 6: This proof is similar to the one given in [12]. By continuity of the determinant we have lim (s)→+∞ det(F (s)) = 1,…”

Section: Appendixmentioning

confidence: 81%

“…To prove this theorem, we slightly adjust the proof from [12]. For any positive η, we denote Z η the set of complex numbers whose distance to the zeros of det(F ) is at most η:…”

Section: Appendixmentioning

confidence: 99%

“…where K uu , K uv , K vu and K vv are defined by equations ( 24)-( 29) and where, similarly to (12), the coefficient K is chosen such that…”

Section: A Control Lawmentioning

confidence: 99%

See 2 more Smart Citations

Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs

Auriol

Aarsnes

Martin

et al. 2018

IEEE Trans. Automat. Contr.

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Norway and DrillWell -Drilling and well centre for improved recovery Stavanger, NorwayWe detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and delay-robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delayrobustness. Indeed, for such systems, using a backstepping-controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence.

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Section: Appendixmentioning

confidence: 81%

“…To prove this theorem, we slightly adjust the proof from [12]. For any positive η, we denote Z η the set of complex numbers whose distance to the zeros of det(F ) is at most η:…”

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs

Auriol

Aarsnes

Martin

et al. 2018

IEEE Trans. Automat. Contr.

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“…It is classic that this result holds when the system is explicit (Salamon 1984;M. Delfour and Karrakchou 1987;Boisgérault 2013). Therefore, to prove the general case, we only need to demonstrate the following lemma:…”

Section: Well-posednessmentioning

confidence: 93%

“…The proof of this theorem is carried out in (Boisgérault 2013) in the case of explicit systems. Here, we expose the proof in the general case.…”

Section: Test In the Laplace Domainmentioning

confidence: 99%

A Core Theory of Delay Systems

Boisgérault¹

2017

Preprint

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We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a practical test for well-posedness based on a graph-theoretic representation of the system; finally, we provide a general stability criterion. We apply each of these results to a structure that commonly arises in the control of delay systems.

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Growth bound of delay-differential algebraic equations

Cited by 2 publications

References 11 publications

Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs

Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs

A Core Theory of Delay Systems

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