In this paper, the authors investigate the problem of designing an observer for Lipschitz nonlinear systems with discrete time measurements (continuous-discrete time systems). The result is based on reachability analysis to synthesize an upper approximation of a reachable set. When this approximation is given in terms of a convex combination of linear mappings, a sufficient condition is given in terms of linear matrix inequality which can be solved using LMI techniques. This approach seems to provide an efficient new tool to address the problem of observer design for a class of Lipschitz systems. An academic example is given to illustrates this point.

This paper concerns observers design for Lipschitz nonlinear systems with sampled output. Using reachability analysis, an upper approximation of the attainable set is given. When this approximation is formulated in terms of a convex combination of linear mappings, a sufficient condition is given in terms of linear matrix inequalities which can be solved employing a linear matrix inequalities solver.This novel approach seems to be an efficient tool to solve the problem of observer synthesis for a class of Lipschitz systems of small dimensions.