Order Extension of Nonlinear Systems for Observer Design under Reduced Observability Properties

Nonlinear unforced systems of order n with reduced observability properties are considered. This reduction concerns the fact that the r-observability map is injective only for r > n. An immersion into a higher order system containing the original system coordinates is proposed, such that estimation of the original states of the system is simplified. Approximate or event-based observers are proposed when some properties are lost for the extension, e.g. smoothness or continuity. Observer design is illustrated by examples and a simplified model of an aerobic bioreactor.