Some Numerical Challenges in Control Theory

We discuss a number of novel issues in the interdisciplinary area of numerical linear algebra and control theory. Although we do not claim to be exhaustive we give a number of problems which we believe will play an important role in the near future. These are: sparse matrices, structured matrices, novel matrix decompositions and numerical shortcuts. Each of those is presented in relation to a particular (class of) control problems. These are respectively: large scale control systems, polynomial system models, control of periodic systems, and normalized coprime factorizations in robust control.