A New Parametrization of Linear Observers

The estimation of unknown variables of a system, the plant, based on a set of known or measured variables is a fundamental and widely studied problem of system theory. We investigate observers that solve this task in the behavioral setting. Our framework includes the discrete and the continuous linear time-invariant cases, and various notions of when a signal is considered to be small. We characterize the observers that guarantee a small estimation error as those containing the “essential part” of the plant behavior. A constructive one-to-one parametrization of all such observers follows naturally from this result.