H∞ controller order reduction due to stable invariant zeros and its application to a magnetic suspension system

This paper studies the H_∞ controller order reduction due to the stable invariant zeros and its application to a magnetic suspension system. First, we explore the H_∞ controller order reduction due to the stable complex invariant zeros to address how we can go beyond the known results for the order reduction due to the unstable or real stable invariant zeros. We propose sufficient conditions for the existence of the reduced-order H_∞ controllers due to the stable complex invariant zeros. If the proposed sufficient conditions are satisfied, we present two LMI based procedures to compute the reduced order H_∞ controllers. Second, we address the application of these theoretical results to a mixed sensitivity problem for a magnetic suspension system with a flexible beam. The numerical computations of the reduced-order controllers and the comparison with the full-order controllers are reported. The numerical investigation carried out validates the proposed theoretical results.