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

Abstract

Summary 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 = Uh+Up, where Uh ranges in the set of all solutions of the associated homogeneous problem, and Up is a particular solution. We present a new solution for Up and prove that it is actually the minimal scriptH2‐norm interpolant in the set of all interpolants. We apply these results in system modeling and in optimal scriptH∞ control of one‐block plants, with a prescribed bound on the distance to instability of the closed‐loop system. The applications are illustrated by examples. Interesting connections to the augmented basic interpolation problem, to Nehari's problem, and to the stability of one‐block plants with multiple unstable invariant zeros are given. Copyright © 2015 John Wiley & Sons, Ltd.