Optimal boundary interpolation and one-block optimal control problem with invariant zeros on the imaginary axis and infinity

Abstract

We formulate a matrix interpolation problem with existing interpolation points on the imaginary axis and infinity and existing equal left and right interpolation points, using the concept of parametrisation of stabilising controllers. Then, we solve the problem of obtaining all its solutions. If interpolation points at infinity are absent, we show that the introduced problem is equivalent to the existing one. We apply this result to solve the problem of optimal interpolation with existent interpolation points on the imaginary axis and infinity. We show by an example that the solution of optimal interpolation is directly applicable to the one-block optimal control with existent invariant zeros on the imaginary axis and infinity. It is seen from the example that not only the transfer matrix of the closed-loop system is constrained on the extended imaginary axis, but also its derivatives.