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- Alexandre Seuret, Frédéric Gouaisbaut
- Automatica
- 2013

In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms linear matrix inequalities (LMI). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability… (More)

- Alexandre Seuret, Frédéric Gouaisbaut, Emilia Fridman
- IEEE Transactions on Automatic Control
- 2015

This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated Jensen inequality employed in the context of discrete-time delay systems. This inequality is a discrete-time… (More)

In this note, we provided an improved way of constructing a LyapunovKrasovskii functional for a linear time delay system. This technique is based on the reformulation of the original system and a discretization scheme of the delay. A hierarchy of Linear Matrix Inequality based results with increasing number of variables is given and is proved to have… (More)

Stability of time delay systems is investigated considering the delay-dependent case. The system without delays is assumed stable and conservative conditions are derived for finding the maximal delay that preserves stability. The problem is treated in the quadratic separation framework and the resulting criteria are formulated as feasibility problems of… (More)

- Frédéric Gouaisbaut, Michel Dambrine, Jean-Pierre Richard
- 2001 European Control Conference (ECC)
- 2001

In this paper, a sliding mode controller is designed for systems with multiple state delays and submitted to additive pertubations. The conditions for the existence of the sliding regime are studied by using Liapunov-Krasovskii functionals. Upper-bound of the delays are obtained by solving a convex minimisation problem expressed in terms of LMIs. Finally,… (More)

- Yassine Ariba, Frédéric Gouaisbaut
- 2007 46th IEEE Conference on Decision and Control
- 2007

Stability analysis of linear systems with time- varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the… (More)

- Dimitri Peaucelle, Denis Arzelier, Didier Henrion, Frédéric Gouaisbaut
- Automatica
- 2007

Topological separation is investigated in the case of an uncertain time-invariant matrix interconnected with an implicit linear transformation. A quadratic separator independent of the uncertainty is shown to prove losslessly the closed-loop well-posedness. Several applications for descriptor systems are then given. First, some known results for stability… (More)

- Yassine Ariba, Frédéric Gouaisbaut
- Int. J. Control
- 2009

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modeling of the delay system. New types of Lyapunov Krasovskii functionals are then proposed allowing to reduce the conservatism of the… (More)

- Frédéric Gouaisbaut, Dimitri Peaucelle
- Proceedings of the 45th IEEE Conference on…
- 2006

This paper is dedicated to the stability of linear time-delay system for a non small delay h. This is motivated by the fact that in some cases introducing a delay in the loop may stabilize a system. Compared to previously derived results the methodology is totally new and the resulting LMI formulas are original contributions. The derived criteria are based… (More)

- Alexandre Seuret, Frédéric Gouaisbaut
- Systems & Control Letters
- 2015

Assessing stability of time-delay systems based on the Lyapunov-Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on the design of more and more involved class of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at… (More)