μ-Interaction Measure for Unstable Systems

The requirement that the system and its block diagonal elements have the same unstable poles limits the applicability of μ interaction measure (μ-IM) to stable systems. We propose an extension of the conventional μ-IM to overcome this difficulty. The decentralized controller is designed based on a block diagonal approximation that is different from the block diagonal elements and is selected by minimizing the scaled L
_∞
distance between the system and the approximation. We also present a simple method for designing the decentralized controller based on the approximation. The proposed method is useful for system stabilization using independent designs of the decentralized controller