Exponential estimates for retarded time-delay systems: an LMI approach

Mondié, Sabine; Kharitonov, Vladimir L.

doi:10.1109/tac.2004.841916

Cited by 171 publications

(116 citation statements)

References 15 publications

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“…System (14) is said to be exponentially stable [14], [16] with a decay rate α > 0 and an exponential gain β ≥ 1 if the following exponential bound holds:…”

Section: A Exponential Stability Of the Reduced Order Systemmentioning

confidence: 99%

Static Output Feedback Sliding Mode Control Design via an Artificial Stabilizing Delay

Seuret

Edwards

Spurgeon

et al. 2009

IEEE Trans. Automat. Contr.

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Abstract-It is well known that for linear, uncertain systems, a static output feedback sliding mode controller can only be determined if a particular triple associated with the reduced order dynamics in the sliding mode is stabilisable. This paper shows that the static output feedback sliding mode control design problem can be solved for a broader class of systems if a known delay term is deliberately introduced into the switching function. Effectively the reduced order sliding mode dynamics are stabilized by the introduction of this artificial delay.

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“…System (14) is said to be exponentially stable [14], [16] with a decay rate α > 0 and an exponential gain β ≥ 1 if the following exponential bound holds:…”

Section: A Exponential Stability Of the Reduced Order Systemmentioning

confidence: 99%

Static Output Feedback Sliding Mode Control Design via an Artificial Stabilizing Delay

Seuret

Edwards

Spurgeon

et al. 2009

IEEE Trans. Automat. Contr.

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“…The norm · W is sightly different from the one of Mondie and Kharitonov (2005) who do not consider a norm depending on the derivativeẋ. This problem has also been dealt by Fridman (2014) by introducing the sum and not the maximum.…”

Section: System Datamentioning

confidence: 93%

“…Since one of the first article by Mori et al (1982) on exponential convergence of time-delay systems, several exponential estimates emerged from the literature: Mondie and Kharitonov (2005), Xu et al (2006) or more recently Trinh et al (2016). But only a few of them used the Wirtingerbased inequality developed by Seuret and Gouaisbaut (2013) to help synthesize observers or controllers for a discrete or distributed delay system.…”

Section: Introductionmentioning

confidence: 99%

Wirtinger-based Exponential Stability for Time-Delay Systems

2017

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This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided. Variations of this theorem for synthesis of a controller or for an observer-based control is derived. Some numerical comparisons are proposed with existing theorems of the literature and comparable results are obtained but with an extension to stabilization.

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“…Consider the definition of exponential stability: Definition 1. Mondié and Kharitonov [2005] System (7a) is exponentially stable with a decay rate δ > 0 if there exists a gain γ ≥ 1 such that the solution z 1 (t,t 0 , φ ) of (7a), starting at time t 0 from any initial condition φ ∈ C 1 , satisfies |z 1 (t,t 0 , φ )| < γ|φ | τ e −δ (t−t 0 ) .…”

Section: Convergence Ratementioning

confidence: 99%

“…Few papers examine the convergence rate of such systems Liu [October 2003], Mondié and Kharitonov [2005], Xu et al [2006]. In this paper, we focus on the tools developed in , Xu et al [2006] to introduce exponential stability criteria and in Fridman and Shaked [2002] to consider one of the less conservative lemmas for the stability of time-delay systems.…”

Section: Convergence Ratementioning

confidence: 99%

Consensus of double integrator multi-agents under communication delay

Seuret

Dimarogonas

Johansson

2009

IFAC Proceedings Volumes

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This paper deals with the consensus problem under network induced communication delays. It is well-known that introducing a delay generally leads to a reduce of the performance or to instability. Thus, investigating the impact of time-delays in the consensus problem is an important issue. Another important issue is to obtain an estimate of the convergence rate, which is not straightforward when delays appear in the network. In this paper, the agents are modelled as double integrator systems. It is assumed that each agent receives instantaneously its own output information but receives the information from its neighbors after a constant delay. A stability criterion is provided based on Lyapunov-Krasovskii techniques and is expressed in terms of LMI. An expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval is derived. The results are supported through several simulations for different network symmetric communication schemes.

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Exponential estimates for retarded time-delay systems: an LMI approach

Cited by 171 publications

References 15 publications

Static Output Feedback Sliding Mode Control Design via an Artificial Stabilizing Delay

Static Output Feedback Sliding Mode Control Design via an Artificial Stabilizing Delay

Wirtinger-based Exponential Stability for Time-Delay Systems

Consensus of double integrator multi-agents under communication delay

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