scispace - formally typeset
Search or ask a question
Book

Stability of Time-Delay Systems

TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
Abstract: Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
05 Mar 2007
TL;DR: This work reviews several recent results on estimation, analysis, and controller synthesis for NCSs, and addresses channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts.
Abstract: Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

3,748 citations


Cites methods from "Stability of Time-Delay Systems"

  • ...R and a positive constant for which Vð Þ ð0Þk k2; dVðxtÞ dt )))) xt¼ ð0Þk k2; 8 2 C ½ max; 0 ;Rnð Þ where the (total) derivative is taken along solutions to (46). h To study the stability of (46), Yue et al. [78] use the following Lyapunov–Krasovskii functional: VðxtÞ ¼ xðtÞ0PxðtÞ þ Z t t max Z t s _xðvÞ0T _xðvÞdvds with symmetric matrices P 9 0 and T 9 0....

    [...]

  • ...Naghshtabrizi and Hespanha [40] use the following Lyapunov–Krasovskii functional to analyze this system VðetÞ ¼ eðtÞ0P1eðtÞ þ Z t t max Z t s _e0ðvÞR _eðvÞdvds þ Z t t min e0ðsÞSeðsÞds where P1 9 0, R 9 0, S 9 0....

    [...]

  • ...Theorem 14 Lyapunov–Krasovskii [13]: The DDE...

    [...]

  • ...However, the Lyapunov–Krasovskii theorem generally leads to less conservative results....

    [...]

  • ...This means that an NCS with a maximum number of consecutive dropouts equal to m is still a DDE like (46), (47), but with min :¼ min k2N f kg; max :¼ max k2N ftkþ1þm tk þ kþ1þmg: The Lyapunov–Krasovskii and the Razumikhin theorems [11], [13], [55] are the two main tools available to study the stability of DDEs of the form of (46) and (47)....

    [...]

Journal ArticleDOI
TL;DR: This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables, comparable to thosebased on the Jensen inequalityLemma.

2,248 citations

Journal ArticleDOI
TL;DR: An alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities is proposed and it is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions.

1,791 citations

Journal ArticleDOI
TL;DR: A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modeled as a nonlinear time-delay system with two successive delay components in the state and the problem of network-based H"~ control is solved accordingly.

1,143 citations

Journal ArticleDOI
TL;DR: Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account, which are less conservative than existing ones.

1,069 citations


Cites background or result from "Stability of Time-Delay Systems"

  • ...(9) are set to zero, and Z='I (' is a suTciently small positive scalar), then Theorem 2 is identical to the well-known delay-independent stability criterion in and Gu et al. (2003) (Proposition 5....

    [...]

  • ...Furthermore, the new criteria also contain the well-known delay-independent stability condition in Gu, Kharitonov, and Chen (2003) and Hale and Verduyn Lunel (1993)....

    [...]

  • ...(9) are set to zero, and Z='I (' is a suTciently small positive scalar), then Theorem 2 is identical to the well-known delay-independent stability criterion in and Gu et al. (2003) (Proposition 5.14 on p. 169) and Hale and Verduyn Lunel (1993) (Eq....

    [...]

References
More filters
Book
Vladimir Vapnik1
01 Jan 1995
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Abstract: Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

40,147 citations

Book
01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Abstract: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.

40,020 citations

Book
01 Jan 1983

34,729 citations


"Stability of Time-Delay Systems" refers methods in this paper

  • ...The matrix background for this section is readily found in many texts; we refer to Golub and Van Loan [81], Horn and Johnson [122]....

    [...]

Book
01 Jan 1985
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.

23,986 citations