Design of global and local state estimators for bilinear Persidskii systems

This paper introduces two state estimators for a class of Persidskii systems that contain bilinear cross-terms in the state, involving nonlinear functions and unknown input. One observer is local, assuming that the state trajectories are small, while the other is designed to be global, considering that the state takes nonnegative values only. The analysis of the estimation error is based on the input-to-output stability theory and the conditions are formulated using linear matrix inequalities. To illustrate our results, we provide simulations for a model of a chemical exothermic reactor and a consumer-resource interaction model.