A moving horizon ℋ∞ observer for discrete-time systems

In this paper, we address the problem of robust moving horizon observer for nonlinear discrete-time systems. The main contribution lies in the use of a robust moving horizon approach in a Luenberger structure observer. Thanks to this new design, a new nonrestrictive synthesis condition, expressed in term of Bilinear Matrix Inequality (BMI), is obtained. Indeed, the obtained BMI contains more degree of freedom than those established by the approaches available in the literature which consider a traditional ℋ_∞ observer, with only one measurement. In this paper, we consider first the linear noisy case, then an extension to nonlinear systems is given. Finally, numerical examples show the better performances of our approach.