| The design of globally convergent observers; for a given class of nonlinear systems, is the main objective of this work. We start by characterizing this class of nonlinear systems, which provide a model for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type, and analyze its dynamics and stability properties. For the system with outputs, a necessary and sufficient condition for detectability is established.; Two explicit observer constructions are proposed in this work, both of which are shown to be globally convergent. The state-estimator design is based on input to state stability (ISS) estimates for the observer driven by the measurements, and the ISS framework together with Lyapunov techniques provide stability and other desirable robustness properties, such as insuring global convergence under sampled outputs, and robustness with respect to noise in the measurements. A notion of robustness with respect to perturbations in the parameters of the system is formulated following ISS ideas, and it is shown that the observers also exhibit robustness in this sense.; Finally, an experiment is reported in which data pertaining to a reversible chemical reaction was collected through an NMR spectrometer. The main observer is implemented and its performance validated against these data. In addition, several numerical tests explore and illustrate the various robustness properties, and a comparison with standard observer constructions (extended Kalman filters, and extended Luenberger observers) is provided. |
