Distance measures for linear systems with multiplicative and inverse multiplicative uncertainty characterisation

Input multiplicative and output inverse multiplicative uncertainty characterisations are common in the robust control literature. We present specialised distance measures and robust stability margins for these types of uncertainty, and derive both robust stability and robust performance theorems, based on the generic distance measure framework of. The uncertainty is allowed to belong to the space ℛℒ_∞, and hence includes unstable systems. This constitutes a significant advance over previous robust stability results for such uncertainty structures, which were valid only for systems in ℛℋ_∞.