The Generalized Hessenberg Representation and Near Unobservability in Model Reduction

The Generalized Hessenberg Representation (GHR) of a linear time invariant system has been proposed as a model reduction method by identifying weakly observable states. This characterization has recently been made precise by the introduction of the concept of Near unobservability. In this paper the GHR is discussed as a model reduction tool. It is related to modal reduction methods and Moore\´s balancing techniques via the reachability/observability gramians. The result of this unified treatment is a set of guidelines for producing a "good" reduced order model.