Pith. Sign in

RECORD

An Improved Stability Method for Linear Systems with Fast-Varying Delays

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Eugenii Shustin, Emilia Fridman

Optimization and Control · Submitted 15 Nov 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As a result, improved frequency-domain and time-domain stability criteria are erived for systems with the delay derivative greater than 1.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0511375 (version 2)
Pith IDTYVGVJMH, Pith's permanent record of this paper and its review
CitationEmilia Fridman, Eugenii Shustin. "An Improved Stability Method for Linear Systems with Fast-Varying Delays." arXiv:math/0511375 (2005). https://pith.science/paper/TYVGVJMH
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,928 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.39 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the $L_2$-norm of a certain integral operator. There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving an operator bound which is an increasing and continuous function of the delay derivative upper bound $d \geq 1$. For $d\to \infty$ the new bound corresponds to the second case and improves the existing bound. As a result, improved frequency-domain and time-domain stability criteria are erived for systems with the delay derivative greater than 1.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. background 0.88 0.33 0.04 asserted 0.97
s1 An input-output approach to stability of such systems is known to be based on the bound of the $L_2$-norm of a certain integral operator. background 1.00 0.05 0.03 asserted 0.96
s2 There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. background 0.94 0.07 0.05 asserted 1.00
s3 In the present note we fill the gap between the two cases by deriving an operator bound which is an increasing and continuous function of the delay derivative upper bound $d \geq 1$. contribution 0.84 0.96 0.41 asserted 1.00
s4 For $d\to \infty$ the new bound corresponds to the second case and improves the existing bound. result 0.92 0.85 0.21 asserted 1.00
s5 As a result, improved frequency-domain and time-domain stability criteria are erived for systems with the delay derivative greater than 1. result 0.96 0.93 0.79 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the $L_2$-norm of a certain integral operator. There exists a bound on this operator in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving an operator bound which is an increasing and continuous function of the delay derivative upper bound $d \geq 1$. For $d\to \infty$ the new bound corresponds to the second case and improves the existing bound. As a result, improved frequency-domain and time-domain stability criteria are erived for systems with the delay derivative greater than 1.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.