Interpolation with strongly F-positive real matrix and application to strong stabilization

Abstract

Necessary and sufficient condition for the newly introduced problem to find a strongly F-positive real rational interpolant for a two-sided interpolation problem are given, for some matrix F to-be-found, as well as the set of all solutions. The strong F-positive realness of the interpolant H implies that H is bi-stable and bi-proper. Since such an interpolant is needed in the strong stabilization problem, the interpolation result is used to develop a control design algorithm, so that a stable stabilizing controller is constructed using the matrices F and H. It is shown (also by examples) that the algorithm works with large-scale plants possessing both real and complex invariant zeros in ℜ[s]≥0. The design algorithm is applied to the sugar mild process, and it is shown that the obtained controller is more suitable for practical implementation, in respect to the literature. By a simple analogy, it is shown that a minimum-phase stabilizing controller can be found by the same interpolation algorithm.