Graphs of linear systems and stabilization

The authors show how geometric ideas can be applied in control theory and in particular in robust control in order to give further insight into of fundamental issues. It is shown that stability criteria for control systems can be stated in terms of geometric notions in the Hilbert space. Two ways of modeling uncertainty in robust control have received a considerable amount of attention: uncertainty in the gap metric and coprime factor perturbations. The connection between these two uncertainty descriptions is discussed. A result is given that gives a full characterization of the maximal ball in the gap metric that can be stabilized by a controller