Extended LMI characterizations for stability and performance of linear systems

Over the past ten years, extensive research has been devoted to extended LMI characterizations for stability and performance of linear systems. These characterizations constitute a valuable tool for reducing conservatism in hard problems like multi-objective control, and robust stability and performance analysis. The present paper proposes a general, projection lemma based methodology for deriving such extended LMIs and hereby provides a straightforward and unified proof for all known literature results as well as some currently missing extended LMIs.