LMI results for resilient state-feedback with H∞ performance

A new approach has been exposed recently for the synthesis of sets of controllers. Among other features, this approach handles the fragility problem. These promising results, developed for static-output feedback synthesis, suffer from being formulated as non convex optimisation problems. The aim of the article is to explore the distinctive case of state-feedback control. Convex LMI optimisation problems are derived for resilient (non-fragile) control with H_∞ guaranteed performance. The essential contribution is that well-known LMI results for state-feedback design can be easily extended to the design of resilient control.