Chained Aggregation and Control System Design:; A Geometric Approach.

摘要

This thesis is an indepth study of the Generalized Hessenberg Representation (GHR) of a linear time-invariant control system. It is shown that the GHR explicitly exhibits a sequence of observability subspaces. By studying these subspaces in this specific basis, a number of results follow. Having defined the subspace algebraically, the authors introduce a topology into the subspaces of state space. Using the GHR they are able to estimate distances between key subspaces. This leads to a measure of the degree of observability, called here near unobservability, which formalizes the intuitive geometric notion that a system is 'nearly unobservable' if it has an invariant subspace near the null space of C. The relationship to other measures of observability is discussed as well as its role in model reduction.