A new parametrization of observers

This paper extends and generalizes recent results on the characterization and parametrization of observers for linear systems in the behavioral framework. We formulate the results in the language of quotient signal modules that was developed by Oberst and first used in the context of observer theory by the first author. The resulting characterization of observers in terms of a generalized internal model principle is both elegant and concise. It includes all such results known to the authors as special cases, including the classical results for linear time-invariant state space systems. Moreover, this new characterization of observers leads to a clean and simple one-to-one parametrization result with only free parameters. This new parametrization allows to decide certain additional observer properties (such as input/output structure or nonintrusiveness) purely by inspection.