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
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 stability criterion. Delay dependent stability conditions are then formulated in terms of linear matrix inequalities (LMI). Finally, several examples show the effectiveness of the proposed methodology.
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