Analytic approximation of rational matrix functions

Abstract:

I am going to speak about joint results with V. I. Vasyunin. We consider the problem of finding the very best (superoptimal) approximation of a given rational matrix functions by matrix functions analytic in the unit disk. The superoptimal approximant must also be rational.

It is a very important problem in control theory to estimate its degree. We have solved a problem that remained open for over 15 years.

We have obtained definitive results in the case of matrix functions of size 2 x 2.