Robust Stability of Distributed Delay Systems

Münz, Ulrich; Rieber, Jochen M.; Allgöwer, Frank

doi:10.3182/20080706-5-kr-1001.02091

Cited by 8 publications

(6 citation statements)

References 21 publications

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“…We choose a suitable LyapunovKrasovskii functional and reformulate the resulting parametric matrix inequality using the full-block S-procedure and a convex-hull relaxation in terms of a LMI. Similar arguments have been used in our previous publications [17], [20], [21] that consider distributed delays in the state. Here, we extend these concepts to systems with distributed input delays.…”

Section: Introductionmentioning

confidence: 68%

Stabilization of linear systems with distributed input delay

Goebel

Münz

Allgöwer

2010

Proceedings of the 2010 American Control Conference

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This paper presents linear matrix inequality (LMI) conditions to design stabilizing state-feedback controllers for linear systems with distributed input delays. A LyapunovKrasovskii functional approach is used and the obtained parametric matrix inequalities are reformulated as LMIs using the full-block S-procedure and a convex hull relaxation. These LMI conditions can be used, for example, to design stabilizing controller for networked control systems (NCS). In this setup, the kernel of the distributed input delay describes the probability density of the packet-delay in the communication channel. This controller design for NCS is illustrated in an example.Index Terms-Time delay systems, distributed input delay, stabilization, full-block S-procedure, convex hull relaxation, networked control systems.

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Section: Introductionmentioning

confidence: 68%

Stabilization of linear systems with distributed input delay

Goebel

Münz

Allgöwer

2010

Proceedings of the 2010 American Control Conference

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“…Note that d in h d (τ ) must be positive even numbers and the functions in h d (τ ) are not orthogonal over [−r, 0] thus the associated F for h d (τ ) is not a diagonal matrix. Since 0.33 > 0, thus the method in Münz et al (2008) cannot be applied. Furthermore, since φ 1 (τ ) = sin(cos(12τ )) does not satisfy the "differentiation closure" property as in (3), the method in Feng & Nguang (2016b) cannot handle (87).…”

Section: Stability Analysis Of a Distributed Delay Systemmentioning

confidence: 99%

Dissipative delay range analysis of coupled differential–difference delay systems with distributed delays

Feng

Nguang

2018

Systems & Control Letters

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This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential-difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains many models of linear delay systems as special cases. A novel Liapunov-Krasovskii functional with non-constant matrix parameters, which are related to the delay value polynomially, is applied to derive stability conditions. By constructing this new functional, sufficient conditions in terms of robust linear matrix inequalities (LMIs) can be derived, which guarantee range stability of a linear CDDS subject to dissipative constraints. To solve the resulting robust LMIs numerically, we apply the technique of sum of squares programming together with matrix relaxations without introducing any potential conservatism to the original robust LMIs. Furthermore, the proposed methods can be extended to solve delay margin estimation problems for a linear CDDS subject to prescribed dissipative constraints. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.

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“…Hence, Theorem 2 can be applied, adapting the scalar λ in (13). The stability condition in [17] states that (17) is stable for a delay interval h up to 5.2. The result in this paper is able to find out a larger delay interval (for which the system remains stable): h = 7.8 for r = 2 and h = 8 for r = 4.…”

Section: Examplementioning

confidence: 99%

Stability of distributed delay systems via a robust approach

Gouaisbaut

Ariba

Seuret

2015

2015 European Control Conference (ECC)

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This paper is dedicated to the stability analysis of a class of distributed delay systems with a non constant kernel. By the use of appropriate orthogonal polynomials, this kernel is expressed as the sum of a polynomial and an additive bounded function. The resulting system is then modeled by an interconnected system between a nominal finite dimensional linear system and a infinite dimensional system. This last system is considered as a structured uncertainty and embedded into some well defined structured uncertainties. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. Finally, numerical examples show the effectiveness of the proposed method.

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Robust Stability of Distributed Delay Systems

Cited by 8 publications

References 21 publications

Stabilization of linear systems with distributed input delay

Stabilization of linear systems with distributed input delay

Dissipative delay range analysis of coupled differential–difference delay systems with distributed delays

Stability of distributed delay systems via a robust approach

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