On robust observer design for a class of time-varying continuous-and discrete-time Persidskii systems

International audienceThis paper considers the state estimation problem for a class of non-autonomous nonlinear systems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach in both continuousand discrete-time scenarios. The requirements are formulated using Linear Matrix Equalities (LME) and Inequalities (LMI). We present two possible applications of the result, a reducedorder observer (e.g., an observer for unmeasured states) and regression in linear and nonlinear, continuous-and discretetime settings. With nonlinear regression being a sophisticated case, the parameter estimation problem for a particular output equation (when the fusion of linear and nonlinear sensors is weighted) is investigated. Two nonlinear examples demonstrating the efficiency of results are provided