CIRCLE CRITERION OBSERVER DESIGN FOR A CLASS OF NONLINEAR SYSTEMS WITH BAD TRAJECTORIES

摘要

A necessary condition for the existence of global observers is the detectability of the plant, i.e. the convergence of indistinguishable trajectories. If non converging indistinguishable trajectories exist, i.e. so called bad trajectories, then no (strong) observer exists. In this paper weak observers are proposed for a class of systems that can have bad trajectories. The convergence is assured for a set of plant's trajectories that excludes the bad ones. This set is characterized by conditions on the plant's trajectories that resembles and generalizes the persistently exciting conditions, well-known in the identification and adaptive control literature.