Shamiur Rahman Ramim: State-Space Realization and Model-Order Reduction: Modeling under Complexity Constraints

Abstract: This thesis deals with the problems of (1) realization (2) partial realization and (3) approximate realization. Focus is directed towards the partial realization problem, which asks for an internal model description for a linear dynamical system provided we only know partial information about its input-output behavior. We study two aspects of this problem: construction and complexity of models, which is measured by the number of equations needed to describe the system. The construction of an internal model description from partially known input-output behavior is fairly trivial but the construction of a simple one is not. We emphasize two methods: one where we treat the problem as one of interpolation and one where we decompose an already known model to a simpler one. If our simplest model is still too complex for any simulation, analysis or controller-synthesis to be made, we turn to the problem of approximate realization in which we find models of lower complexity that approximate the behavior. We treat this approximation problem as a problem of structured low-rank approximation. This all can be seen as a model-order reduction procedure where we make the model smaller while keeping -- or in this case, approximating -- some desirable attribute.