Robust H₂ control with regional stability constraints

The problem of static state feedback robust H₂ control with regional stability constraints for the closed-loop system is considered. Both continuous and discrete-time systems with polytopic uncertainty are investigated. A new LMI-based sufficient condition for the existence of parameter-dependent Lyapunov functions is proposed. Static state feedback controllers required are not only guaranteed to satisfy all closed-loop poles to stay inside a specified region for all admissible parameter uncertainties, but also provide an upper bound for the H₂ cost function, which is minimized using LMI convex optimization approach.