-Interaction Measure for Unstable Systems

In this paper, we present a method for system stabilisation through independent designs of the decentralised controller. The proposed method extends the practical applicability of the conventional μ interaction measure (μ-IM) to unstable systems. The decentralised controller is designed based on a block diagonal approximation 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 suboptimally selected by minimising the scaled L∞ distance between the system and the approximation. We present a numerical method for choosing the block diagonal approximation and a simple method for designing the decentralised controller based on the approximation.