μ-interaction measure for unstable systems

In this paper, we present a method for system stabilization through independent designs of the decentralized controller. The proposed method extends the practical applicability of the conventional μ interaction measure (μ-IM) to unstable systems. The decentralized controller is designed based on a block diagonal approxi- mation that is different from the block diagonal elements, but has the same number of unstable poles as the system. By expressing the μ-IM in terms of the transfer matrix between the disturbances and inputs, we show that the block diagonal approximation can be sub-optimally selected by minimizing the scaled L-inf distance between the sys- tem and the approximation. We present a numerical method for choosing the block diagonal approximation and a simple method for designing the decentralized controller based on the approximation.Accepted versio