Robust non-fragile LQ controllers: The static state feedback case

This paper describes the synthesis of non-fragile or resilient regulators for linear systems. A general framework for fragility is described using state-space methodologies, and the LQ/H₂ static state-feedback problem is examined in detail. We discuss the multiplicative structured uncertainties case, and propose remedies of the fragility problem using an optimization programming framework via matrix inequalities. A special case that leads to a convex optimization framework via linear matrix inequalities (LMIs) will be considered. The benchmark problem is taken as an example to show how special controller gain variations can affect the performance of the closed-loop system.