State space methods for tangential interpolation problems

State space methods for solving tangential interpolation problems for matrix functions in a given class have been developed extensively. These are interpolation problems in which the values in certain directions of the interpolant matrix functions, and several of their derivatives, are prescribed at given points in the complex plane. For the most part, the matrix functions under consideration are rational functions or polynomials (perhaps with symmetries); however, other important classes of matrix functions have been studied as well, notably, the Nevanlinna classes on the unit disk and the upper half-plane, and the Hardy class H₂ on the unit disk. This development is motivated by many important applications in systems and control. We present some recent results and open problems in this area