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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)

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)

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)

- Alexandre Seuret, Frédéric Gouaisbaut, Emilia Fridman
- IEEE Trans. Automat. Contr.
- 2015

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

- Yassine Ariba, Frédéric Gouaisbaut
- CDC
- 2007

Stability analysis of linear systems with timevarying 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, Michel Dambrine, Jean-Pierre Richard
- Systems & Control Letters
- 2002

This paper considers the sliding mode control of uncertain systems with single or multiple, constant or time-varying state-delays, submitted to additive perturbations. The sliding surface is designed so to maximize the calculable set of admissible delays. The conditions for the existence of the sliding regime are studied by using LyapunovKrasovskii… (More)

This paper considers the robust stability of time delay systems by means of quadratic separation theory. Using this formalism both delay independent and delay dependent criteria are provided. In the nominal case, without uncertainties, our result is shown to be equivalent to other LMI-based results from the literature. Finally, an academic example is… (More)

We investigate the stability analysis of linear timedelay systems. The time-delay is assumed to be a time-varying continuous function belonging to an interval (possibly excluding zero) with a bound on its derivative. To this end, we propose to use the quadratic separation framework to assess the intervals on the delay that preserves the stability.… (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)