On high-gain observer redesign with respect to the nature of the available outputs

This note is devoted to the redesign of a high-gain observer that has been conceived for a class uniformly observable nonlinear systems where the output measurements are assumed to be available continuously in time. The ultimate motivation of this redesign consists in providing an observer structure to properly tackle the problem of sampled output measurements while accounting for an eventual output measurement time delay in the case of continuous-time output measurements as well as in in the case of sampled output measurements. This leads to a unified high-gain observer with a versatile structure that accounts for the different scenarios related to the output measurements availability. A particular emphasis is put on the observer structure bearing in mind the main motivation of the involved observer redesign. Of a primary importance, it is shown that the proposed observer inherits the same properties as its underlying observer using an adequate technical lemma.