Complete type Lyapunov-Krasovskii functionals with a given cross term in the time derivative

Mondié, Sabine; Kharitonov, Vladimir L.; Santos, Omar

doi:10.1109/cdc.2005.1582964

Cited by 21 publications

(19 citation statements)

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“…which corresponds to necessary and sufficient conditions of stability) is constructed by solving a functional differential equation. This approach is useful to derive robustness conditions with respect to delay variations [4] or parameters uncertainties [17], [18].…”

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confidence: 99%

Stabilization of time-delay systems through linear differential equations using a descriptor representation

Seuret

Johansson

2009

2009 European Control Conference (ECC)

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Abstract-In this article, a new method to assess stability and to design static state feedback controller for linear timedelay systems is introduced. The method based on linear differential equations allows considering explicit LyapunovKrasovskii functionals with non constant matrix parameters. The stability conditions considering constant delays are delaydependent and expressed using easy computable linear matrix inequalities. An example is introduced to show the efficiency of the stabilization criteria.

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confidence: 99%

Stabilization of time-delay systems through linear differential equations using a descriptor representation

Seuret

Johansson

2009

2009 European Control Conference (ECC)

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“…The aim of our contribution is to extend to the case of neutral type time delay systems the results on complete type functional with derivative including special cross terms [10] and to use them to obtain instability conditions in the spirit of Ochoa and Mondié [11].…”

Section: Introductionmentioning

confidence: 99%

Instability conditions for neutral type time delay systems

Ochoa

Mondié

2008

2008 47th IEEE Conference on Decision and Control

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“…In reference [16], the candidate Lyapunov functional called complete LKF, leads even to a necessary and sufficient stability condition. Nevertheless, the parameters composing this complete LKF make it numerically difficult to handle, especially for high dimensional systems [14,23]. A lot of investigations then turns to approximating these parameters, and more recently, approximation methods have been improved by considering polynomial like parameters of arbitrary degree [27].…”

Section: Introductionmentioning

confidence: 99%

Tractable sufficient stability conditions for a system coupling linear transport and differential equations

Safi

Baudouin

Seuret

2017

Systems & Control Letters

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This paper deals with the stability analysis of a system of finite dimension coupled to a vectorial transport equation. We develop here a new method to study the stability of such a system, coupling ordinary and partial differential equations, using linear matrix inequalities led by the choice of an appropriate Lyapunov functional. To this end, we exploit Legendre polynomials and their properties, and use a Bessel inequality to measure the contribution of our approximation. The exponential stability of a wide class of delay systems is a direct consequence of this study, but above all, we are detailing here a new approach in the consideration of systems coupling infinite and finite dimensional dynamics. The coupling with a vectorial transport equation is a first step that already prove the interest of the method, bringing hierarchized conditions for stability. We will give exponential stability results and their proofs. Our approach will finally be tested on several academic examples.

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Complete type Lyapunov-Krasovskii functionals with a given cross term in the time derivative

Cited by 21 publications

References 4 publications

Stabilization of time-delay systems through linear differential equations using a descriptor representation

Stabilization of time-delay systems through linear differential equations using a descriptor representation

Instability conditions for neutral type time delay systems

Tractable sufficient stability conditions for a system coupling linear transport and differential equations

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