Speaker
Description
Rational matrices, that is, matrices whose entries are univariate rational functions appear in control problems and also in the numerical solution of non-linear eigenvalue problems as approximations of other matrices whose entries are more general univariate functions. Very often the rational matrices arising in applications have particular structures that should be preserved/used in the numerical computation of their poles, zeros and minimal indices. In this talk, we consider three classes of structured rational matrices R(z) that are Hermitian upon evaluation on (a) the real axis, (b) the imaginary axis, or (c) the unit circle. Our goal is to show how to construct linear polynomial system matrices, i.e., linearizations, for those R(z) that preserve the corresponding structures and are strongly minimal, a property that guarantees that such polynomial system matrices allow for a complete recovery of the poles, zeros, and minimal indices of R(z). Thus, structured generalized eigenvalue algorithms applied to these pencils will allow us to compute all these quantities in a structure preserving manner. We will present several approaches for solving these problems developed by the authors in the last few years.
