A reformulation of augmented basic interpolation problem and an application to H∞H∞ control

In this paper we present a new formulation of the augmented basic interpolation problem (aBIP) with rational matrices, in terms of the stability of four rational matrices, so that the aBIP transforms into a purely linear-algebraic problem. Actually, the existing interpolation condition, given by an integral, is replaced by stability of a rational matrix.The new condition is applied to the H∞H∞ optimal control of one-block plants having imaginary axis invariant zeros. A new parameter in the parametrization of H∞H∞ optimal controllers is revealed, which is given in terms of the derivative of the closed-loop system at the imaginary axis invariant zeros of the plant. The H∞H∞ optimal control algorithm is illustrated by an example, and compared to the existing algorithms.