A convex approach to the output feedback stabilisation problem

We present a convex approach to the static output feedback stabilization problem based on the classical state feedback Lyapunov equation. It is shown that our approach leads to a necessary and sufficient condition for a system to be stabilizable via static output feedback if we take into account all the possible state-space representations of the system. Our approach can be used for designing decentralized controllers and is easily extended to the ℋ₂ , ℋ_∞ and the mixed ℋ₂/ℋ _∞ problems via standard LMI techniques