New interpolation solution and application in system modeling and optimal control with prescribed distance to instability

摘要

We present a system theoretic interpretation of a two-sided interpolation problem with a stable rational matrix U (interpolant) without constraints on its norm. It is known that all solutions U of that problem can be expressed as U = U-h + U-p, where U-h ranges in the set of all solutions of the associated homogeneous problem, and U-p is a particular solution. We present a new solution for U-p and prove that it is actually the minimal H-2-norm interpolant in the set of all interpolants.