A full block S-procedure with applications

We provide a general result that allows us to equivalently translate robust performance analysis specifications characterized through a single quadratic Lyapunov function into the corresponding analysis test with multipliers. As an illustration we apply the technique to robust quadratic and robust generalized H₂ performance, and we comment on the wide range of its applicability. Finally, we reveal how this technique allows us to approach LPV (linear parameter varying) problems in which the control input and measurement output matrix are parameter dependent. The latter is made possible by letting the parameter enter the LPV controller via a kernel representation that generalizes the more conventional LFT structure