Robust Stabilization and H  ∞  Control of Uncertain Distributed Delay Systems

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

doi:10.1007/978-3-642-02897-7_19

Cited by 11 publications

(19 citation statements)

References 33 publications

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“…Various aspects of linear systems with distributed delays have been studied earlier, [26,43,45,46,64,65]. In this paper, by using a frequency domain analysis, we improve the sufficient conditions of [5,52].…”

Section: Introductionmentioning

confidence: 98%

Stability Analysis of Cell Dynamics in Leukemia

Özbay

Bonnet

Benjelloun

et al. 2012

Math. Model. Nat. Phenom.

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Abstract. In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.

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Section: Introductionmentioning

confidence: 98%

Stability Analysis of Cell Dynamics in Leukemia

Özbay

Bonnet

Benjelloun

et al. 2012

Math. Model. Nat. Phenom.

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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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“…Thus, the set of inequalities provided in Corollary 3 represents a more general formulation than these two inequalities. Additionally, the Parseval identity proves that inequality (14) becomes asymptotically non conservative as N goes to infinity.…”

Section: Remarkmentioning

confidence: 96%

“…Another widely used approach in the literature stems from the robust analysis using the same driving forces namely the comparison systems and integral inequalities [15]. In [14], a combined full block S-Procedure and Lyapunov analysis is performed to prove the stability of a distributed delay system with a rational kernel. More recently, using quadratic separation approach, [7] has provided some Linear Matrix inequality (LMI) for polynomial kernels.…”

Section: Introductionmentioning

confidence: 99%

Complete quadratic Lyapunov functionals for distributed delay systems

2015

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International audienceThis paper is concerned with the stability analysis of distributed delay systems using complete-Lyapunov functionals. Numerous articles aim at approximating their parameters thanks to a discretization method or polynomial modeling. The interest of such approximations is the design of tractable sufficient stability conditions. In the present article, we provide an alternative method based on polynomial approximation which takes advantages of the Legendre polynomials and their properties. The resulting stability conditions are scalable with respect to the maximum degree of the polynomials and are expressed in terms of tractable linear matrix inequalities. Several examples of delayed systems are tested to show the effectiveness of the method

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Robust Stabilization and H ∞ Control of Uncertain Distributed Delay Systems

Cited by 11 publications

References 33 publications

Stability Analysis of Cell Dynamics in Leukemia

Stability Analysis of Cell Dynamics in Leukemia

Stabilization of linear systems with distributed input delay

Complete quadratic Lyapunov functionals for distributed delay systems

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