Uniting observers

International audienceWe propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviours for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: one, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behaviour. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented

Local observers design for a class of neural mass models

International audienceWe present a model-based approach to estimate the mean embrane potentials (and their time-derivatives) of populations of neurons within cortical columns. We consider a general class of neural mass models for which we design local state observers. The synthesis relies on linear parameter-varying systems techniques and the observer gains are obtained by solving linear matrix inequalities. Simulations results are presented to illustrate the efficiency of the approach