International audienceThis paper deals with observer-based controller design method via Linear Matrix Inequalities~(LMIs) for a class of switched discrete-time linear systems. The main contribution consists in providing different scenarios of the use of Finsler's Lemma to reduce the conservatism of some previous results in the literature. Thanks to this scenarios and the use of some other new mathematical tools, one of the objectives of this paper is to open new research directions for other control design problems. The validity and effectiveness of the proposed design methodologies are shown through a numerical example

This paper deals with observer-based control design for a class of switched discrete-time linear systems with parameter uncertainties. The main contribution of the paper is to propose a convenient way based on Finsler's lemma to enhance the synthesis conditions, expressed in terms of Linear Matrix Inequalities (LMIs). Indeed, this judicious use of Finsler's lemma provides additional decision variables, which render the LMIs less conservative and more general than all those existing in the literature for the same class of systems. Two numerical examples followed by a Monte Carlo evaluation are proposed to show the superiority of the proposed design technique.

This paper deals with observer-based stabilization for a class of Linear ParameterVarying (LPV) systems in discrete-time case. Two new LMI design methods are proposed to design the observer-based controller gains. The first one is based on the use of a Young's relation in a judicious way, while the second one, which provides more interesting results, is based on the use of a general congruence principle. This use of congruence principle leads to some additional slack matrices as decision variables, which make disappear some bilinear terms leading to less conservative LMI conditions. To the authors' best knowledge, this is the first time the congruence principle is exploited in this way. The effectiveness and superiority of the proposed design techniques, compared to existing results in the literature, are demonstrated through two numerical examples.

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Aitouche. A modified twosteps LMI method to design observer-based controller for linear discrete-time systems with parameter Abstract-This note deals with the problem of observerbased stabilization for discrete-time linear systems with normbounded parameter uncertainties. Thanks to slack variable technique and the two-step method, an LMI-based approach is provided to compute simultaneously all the main decision variable of the observer-based controller problem. Our approach is inspired from the classical two-steps method introduced by Stankovic et al. and the modified two-steps method introduced by Zemouche et al.. Some comments are reserved to emphasize and clarify the difference between the different variants of the two-steps method. A numerical example is provided in order to illustrate how the new algorithm is less conservative than previous results in literature.