Discrete-Time Observers for Singularly Perturbed Continuous-Time Systems: Part I, Autonomous Systems

The use of discrete-time observers for nonlinear singularly perturbed continuous-time autonomous systems is explored. Our design approach is based an inversion of state-to-measurement maps. We exploit the two-time-scale nature of the system to construct separate reduced-order observers for the approximate slow and fast sub-systems, using multirate measurements and computation. We compare our reduced-order observers to a full-order observer designed for the same system. Although our reduced-order observers exhibit some approximation error, they also result in reduced computational requirements if the inversion is performed on-line, reduced memory requirements if the inversion is implemented by lookup table, and reduced stiffness. The trade-off between accuracy and implementation requirements always favors our approach for systems with significant separation of time scales.