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Summary This paper deals with the robust observer‐based scriptℋ∞ control design for a class of Lipschitz nonlinear discrete‐time systems with parameter uncertainties. Based on the use of a reformulated Lipschitz property combined with the slack variable techniques and some mathematical artifacts, it is shown that the solution of the discrete‐time output feedback stabilization problem is conditioned by a set of bilinear matrix inequalities, which become linear matrix inequalities by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples are provided to show the validity and superiority of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

International audienceThis paper deals with the problem of observer-based stabilisation for linear systems with structured norm-bounded parameter uncertainties. A new design methodology is established thanks to a judicious use of some mathematical artefacts such as the well-known Young inequality and various matrix decompositions. The proposed method allows one to compute simultaneously the observer and controller gains by solving a single bilinear matrix inequality (BMI), which becomes a linear matrix inequality (LMI) by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples and evaluations of the conservatism are provided to show the effectiveness of the proposed design methodology

Summary This paper presents a new observer‐based controller design method for Lipschitz nonlinear systems with uncertain parameters and scriptL2 ‐bounded disturbance inputs. In the presence of uncertain parameters, the separation principle is not applicable even in the case of linear time invariant systems. A state of the art review for uncertain linear systems is first presented to describe the shortcomings and conservatism of existing results for this problem. Then a new LMI‐based design technique is developed to solve the problem for both linear and Lipschitz nonlinear systems. The features of the new technique are the use of a new matrix decomposition, the allowance of additional degrees of freedom in design of the observer and controller feedback gains, the elimination of any need to use equality constraints, the allowance of uncertainty in the input matrix and the encompassing of all previous results under one framework. An extensive portfolio of numerical case studies is presented to illustrate the superiority of the developed design technique to existing results for linear systems from literature and to illustrate application to Lipschitz nonlinear systems. Copyright © 2016 John Wiley & Sons, Ltd.

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