On Robust Observer Design for a Class of Time-Varying Continuous-Time and Discrete-Time Persidskii Systems

This article considers the state estimation problem for a class of nonautonomous nonlinear systems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach in both continuous- and discrete-time scenarios. The requirements are formulated using linear matrix equalities (LME) and inequalities (LMI). We present two possible applications of the result, a reduced-order observer (e.g., an observer for unmeasured states) and regression in linear and nonlinear, continuous- and discrete-time 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.